(FYI, I wrote this before TMIT and Karadoc posted, and this post doesn't take anything they said into account because at the time I wasn't aware of their posts. I will comment on theirs in a later post, probably.)
Regarding Representation versus Universal Suffrage, I have to admit that it's a sticky issue for me as well. I am leaning in the direction of thinking the nerf to 2 Beakers was not the way to fix the situation (although it was a good and reasonable effort). I'll try to explain why.
First, about me - I used to obstinately run a Pure Specialist economy all the time in unmodded BTS, even on Emperor for a while (usually as either Sitting Bull or Elizabeth) ... so I'll be weighing in on it as someone who has been there and done it ad nauseum, both with and without the Pyramids.
Firstly, I disagree with the statement that a Pure Specialist economy was nonviable as an empire design before the nerf. In regular BTS, the thing about a Pure Specialist economy (on a Phi leader, of course) was that it had a very strong early game (which could be setup with minimal issues on a variety of map starts) coupled with an oddly flexible midgame that emphasized bulbing toward Education and Liberalism and then blazing away on the jet-fueled engine of a massive tech lead while your rivals fumbled around trying to catch up.
The catch though was that a Pure Specialist economy did run into a problem once rival civilizations reached the Industrial and Modern eras. All the Emancipation floating around would start to make your Caste System frown, which would force you to use your Culture Slider more, which would make your cities not give as much research from their Trade Routes ... and all those beefy 7+ Commerce cottages now owned by your rivals around the world (and all that tech trading and tech difficulty reduction stuff that would let them nip at your heels even while you're ahead) would start cutting a great big wedge out of your research-advantage pie.
I guess the biggest trap with the unmodded BTS Pure Specialist economy is in thinking that you should keep growing your cities bigger after you get Biology ... under most circumstances, you shouldn't - getting that much bigger is a nightmare for your healthiness and happiness. What you should do instead is use the extra food as an excuse to start turning some of your farms into Watermills and Workshops in preparation for a switch to State Property and a Hammer/Specialist hybrid economy. Eventually you end up pretty much turning into a Super Hammer Economy with specialists still active in only a few cities (which is also handy for cranking out the inevitable spaceship parts, or Modern Armors and Mobile Artillery, once you get to the point of using your advantage to settle down and win the game). You can stay on Rep through the end of the game in that case (or hop to UniSuff to have the rushbuy option available if you've been building Wealth a lot and would like the added flexibility).
That was what you did to "win" with a Pure Specialist economy. You used it to get a huge tech lead and then evolved your economy into something else. Using your fancy gadgets, you revolutionized your society from a farm-and-philosophers nation into a powerful hammer-heaven that still had a strong core of settled research to back it up.
...And of course, along the way to getting to that "transition" point, you snagged the free tech from Liberalism and probably ate up most of the free great people from Economics/Physics/Communism/Fascism/etc. by beating the other nations to them.
So no, I don't think a Pure Speicalist economy was at all unviable before the nerf - if you used it appropriately and didn't try to make it do something it wasn't good at doing. I do think it is unviable now, after the nerf, because its lategame disadvantages are much harder to make up for in a timely fashion compared to before (because it takes you longer to zoom ahead in the midgame and the rival civs have more time to catch up). K-Mod pretty much forces you to use a Cottage/Specialist Hybrid economy if you would have run a Pure Specialist economy before, which is fine with me in some ways and irritating in others (because if I end up on a map start where cottaging heavily isn't an option, my Phi leaders are inevitably in a worse situation for the midgame than they were pre-nerf).
In my opinion, honestly, it would probably have been better to change the effect of the Pyramids to something different (and by "different" I mean "not highly prone to breaking the game at low difficulty levels and teaching new players the bad habit that wonderspamming is a good idea") than it would have been to nerf Representation's Research benefit. (I might experiment with that in my own private mod-mod of K-Mod and see what happens.)
Hammer/Cottage economies (UniSuff, FreeSpeech, State Property) have always had a ridiculously strong lategame - you seriously can't go wrong with them, if you're lacking in anything you just Wealth or Research process it - even an unexpected defensive war usually gets shrugged off because your production and research are both so high that you can respond to pretty much anything - so it was nice that there used to be a viable alternative that didn't involve Cottage Spam. Now in K-Mod you can choose to Cottage Spam with some specialists on the side, or you can just Cottage Spam hardcore until you get to the inevitable point where Production becomes king.
I dunno, I can't shake feeling like there must've been a better way to encourage hybridization and discourage just sitting on Rep forever. I'm not even going to say that the way it was done was particularly bad - I also thought Rep needed a nerf of some sort for the reasons you gave - but actually playing with it since the nerfs, and noticing how much less I use specialists in general even on Elizabeth, has made me wonder about that.
Regarding Representation versus Universal Suffrage, I have to admit that it's a sticky issue for me as well. I am leaning in the direction of thinking the nerf to 2 Beakers was not the way to fix the situation (although it was a good and reasonable effort). I'll try to explain why.
First, about me - I used to obstinately run a Pure Specialist economy all the time in unmodded BTS, even on Emperor for a while (usually as either Sitting Bull or Elizabeth) ... so I'll be weighing in on it as someone who has been there and done it ad nauseum, both with and without the Pyramids.
Firstly, I disagree with the statement that a Pure Specialist economy was nonviable as an empire design before the nerf. In regular BTS, the thing about a Pure Specialist economy (on a Phi leader, of course) was that it had a very strong early game (which could be setup with minimal issues on a variety of map starts) coupled with an oddly flexible midgame that emphasized bulbing toward Education and Liberalism and then blazing away on the jet-fueled engine of a massive tech lead while your rivals fumbled around trying to catch up.
The catch though was that a Pure Specialist economy did run into a problem once rival civilizations reached the Industrial and Modern eras. All the Emancipation floating around would start to make your Caste System frown, which would force you to use your Culture Slider more, which would make your cities not give as much research from their Trade Routes ... and all those beefy 7+ Commerce cottages now owned by your rivals around the world (and all that tech trading and tech difficulty reduction stuff that would let them nip at your heels even while you're ahead) would start cutting a great big wedge out of your research-advantage pie.
I guess the biggest trap with the unmodded BTS Pure Specialist economy is in thinking that you should keep growing your cities bigger after you get Biology ... under most circumstances, you shouldn't - getting that much bigger is a nightmare for your healthiness and happiness. What you should do instead is use the extra food as an excuse to start turning some of your farms into Watermills and Workshops in preparation for a switch to State Property and a Hammer/Specialist hybrid economy. Eventually you end up pretty much turning into a Super Hammer Economy with specialists still active in only a few cities (which is also handy for cranking out the inevitable spaceship parts, or Modern Armors and Mobile Artillery, once you get to the point of using your advantage to settle down and win the game). You can stay on Rep through the end of the game in that case (or hop to UniSuff to have the rushbuy option available if you've been building Wealth a lot and would like the added flexibility).
That was what you did to "win" with a Pure Specialist economy. You used it to get a huge tech lead and then evolved your economy into something else. Using your fancy gadgets, you revolutionized your society from a farm-and-philosophers nation into a powerful hammer-heaven that still had a strong core of settled research to back it up.
...And of course, along the way to getting to that "transition" point, you snagged the free tech from Liberalism and probably ate up most of the free great people from Economics/Physics/Communism/Fascism/etc. by beating the other nations to them.
So no, I don't think a Pure Speicalist economy was at all unviable before the nerf - if you used it appropriately and didn't try to make it do something it wasn't good at doing. I do think it is unviable now, after the nerf, because its lategame disadvantages are much harder to make up for in a timely fashion compared to before (because it takes you longer to zoom ahead in the midgame and the rival civs have more time to catch up). K-Mod pretty much forces you to use a Cottage/Specialist Hybrid economy if you would have run a Pure Specialist economy before, which is fine with me in some ways and irritating in others (because if I end up on a map start where cottaging heavily isn't an option, my Phi leaders are inevitably in a worse situation for the midgame than they were pre-nerf).
In my opinion, honestly, it would probably have been better to change the effect of the Pyramids to something different (and by "different" I mean "not highly prone to breaking the game at low difficulty levels and teaching new players the bad habit that wonderspamming is a good idea") than it would have been to nerf Representation's Research benefit. (I might experiment with that in my own private mod-mod of K-Mod and see what happens.)
Hammer/Cottage economies (UniSuff, FreeSpeech, State Property) have always had a ridiculously strong lategame - you seriously can't go wrong with them, if you're lacking in anything you just Wealth or Research process it - even an unexpected defensive war usually gets shrugged off because your production and research are both so high that you can respond to pretty much anything - so it was nice that there used to be a viable alternative that didn't involve Cottage Spam. Now in K-Mod you can choose to Cottage Spam with some specialists on the side, or you can just Cottage Spam hardcore until you get to the inevitable point where Production becomes king.
I dunno, I can't shake feeling like there must've been a better way to encourage hybridization and discourage just sitting on Rep forever. I'm not even going to say that the way it was done was particularly bad - I also thought Rep needed a nerf of some sort for the reasons you gave - but actually playing with it since the nerfs, and noticing how much less I use specialists in general even on Elizabeth, has made me wonder about that.