First of all, great list in which i agree with mostly everything. I tried my hand in modding to bring up some of the weaker civs, but in doing so, i've found two civs rated poorly by you which I found difficult to justify too much serious improvements
My comments in Purple
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"1. Assyria
Assyria's advantages are: Siege Towers, Royal Library and Tech stealing.
1. Siege Towers. Some people rave about these, but I think that getting them at Mathematics means that they come too late to be much use on Deity. Maybe I am not playing it properly. I invite comments on this point. They are really powerful on lower difficult levels, broken perhaps. But on Deity, even when I beeline Maths after lux techs, I run into troops that can smash these up. UU rating = 2/5"
I think you underrate this UU, which becomes that much stronger if one goes Honor. I see that you rate the Battering Ram at 4/5 and IMO, the Siege Tower is at least as good as the BR. Yes, they come a little bit later in the tech tree, but I think their usefulness lasts much longer. Rams are great till Medieval, whilst Siege Towers remain useful til the end of the Industrial due to its synergy with crossbows/gatlings/cannons.
They do get mashed up by stronger melee units, but that is much less of a problem if you clear out enemy troops first, and only send in the Siege Tower when you want to rush down a city. Unlike Rams, Siege Towers are meant to work with other units, so its not such a big minus that they require other units to clear out threatening enemy melee units before sending them in (they handle ranged attacks quite well). I gave them 4/5 in my own subjective rating.
"2. Royal library. A minuscule buff for troops when filled with great works. But warmongers want to use GWs and GAs for faster SPs and Golden Ages, respectively. UB rating = 1 (being generous)"
Agreed. This is a really underwhelming UB and I buffed it by taking krajzen's idea of giving it +2 production. (the rationale being that it allows Assyria to generate a decent-sized army faster although it is also useful for less aggressive strategies). After giving it +2 production, I personally rated this UB as 3/5 since the production boost comes so early.
"3. Tech stealing. This can be great if you get something you really want. But a bit hit and miss. UA rating = 2/5."
As you said, its a bit hit-and-miss. Could be great or a little underwhelming so 2/5 is reasonable although I rated it higher at 3/5. All in all, with my buff to RL, I had Assyria as a (4+3+3=10) rating and the only buff i gave them was +2 production in RL.
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"Rome
Rome's advantages are: Legions, Ballistas, and Capital-first building bonus.
1. Legions. These suffer from the same problem as all Classical Era UUs: they just don't cut the mustard on Deity. You won't have caught up to the AI yet, and so waging war with slightly-buffed Swordsmen is not a good idea. They can build roads, but then if they're building roads then they're not farming XP or completing quests or acting as meat shields for CBs/XBs, are they? UU rating = 1/5."
Agreed, although I think a 1.5 rating is probably more accurate (not a disagreement since you use discrete integers in your ratings) which is why I incorporated a mod which gave them a Tetsudo free promotion (+15% defence to ranged attacks). This makes them 2/5 in my own rating.
"2. Ballistas. As above. On lower difficulty levels these could well be great, but laying siege to a Deity AI city with these is liable only to get them one-shotted. Yes they are a bit better than Catapults, which I'm sometimes build if I have nothing better to build, and then they can gather XP before being upgraded to Artillery later, but they're nothing to shout about. UU rating = 1/5."
Agreed, and this is quite underwhelming. At the risk of making it overpowered, I incorporated krajzen's ballista buff (which has some historical accuracy according to him!) which removes the requirement to set up before attack (lost on upgrade of course!). I haven't tested it out, but I tentatively give them a 4/5 rating as they become Siege-Composite Bowmans minus defensive terrain bonuses and limited visibility.
"3. Capital first. I don't know about you but I like the flexibility of being able to build whatever is most effective upon completion, not having to contrive my build order to take into account what I want to start building in my expos when the capital building is complete. Generally, things that you want in all cities (like LIBRARIES) are built at the same time, so I think that this UA is really all about roleplaying, and has about as much bearing on how the game plays out as the story of Romulus and Remus has on the lives of modern Romans. There could be some things later on (Industrial era) when this becomes quite useful, but I can't imagine it being a help in the whole first half of the game. UA rating = 1/5."
This rating seemed problematic to me. Wide empires benefit more than Tall empires, and occasionally Capital locations can be poor, so its tricky to estimate the production boost this gives. That being said, a potential 25% building production boost to non-Capital cities (which are usually lagging in production) seems very significant to me. To get the most of this UA requires the Capital to prioritize buildings or purchase buildings in the Capital so you have to adjust the construction of other stuff like caravans/workers/militaryunits and sometimes spend gold to maximize this UA, but as long as you have a decent Capital, this UA really helps non-Capital cities get their infrastructure up and running.
If one is domination-focused, this UA becomes even stronger, since puppet cities only build buildings. Getting gold, science, happiness and culture buildings in puppet cities, or even ones which you've annexed 25% faster is pretty significant. For me, this UA is 2/5 if one plays peaceful, and 3/5 if one chooses the path of conquest. In total, with my mod buffs, Rome becomes a 2 + 4 + 3 = 9 rating Civ.