As we can raise and stop raising enemy cities to increase happiness, not sure how it is different to 'burn away' unhappiness in your own cities. I would find this more realistic than having a tick box for not being allowed to grow. If there was more opportunity cost involved it would balance out any 'abuse'.
Previously (in the civ series if not civ 5, can't remember exactly) raising cities used to destroy buildings at the same time which seems like a good trade off and seems much more reasonable...Population will not be happy about being 'forcibly displaced' and are like to riot and sack the city. If you burn it to the ground anyway then who cares but if your just getting rid of some 'undesirables' then you have to risk damage to the city while they are removed.
You can add x number of turns of resistance on too while the city settles back down.
As for using it to farm barbarian units. Not sure of the exact timer but rebels spawn every x number of turns when raising a city so you have to burn a lot of population to gain some meagre resources and if this was really worth it why aren't people 'abusing' it now when they burn enemy cities they captured?
Considering we can already raise cities, just not our own i don't see a great difference apart from it takes away another advantage to being a warmonger as being a warmonger you can burn cities to control happiness but as a none warmonger you can't.
I am not saying it's a perfect solution or anything. I have not even voted for (or against) this, yet. But it was more of "I would rather have this then that"; as in I would rather have resettling then being able to raze my own cities. As you note it's a bit weird that we can raze a conquered enemy city at any time; even ages after you captured it. But you can't ever do it to your own, to city-states and to enemy capitals (Holy cities are supposed to be off limits, don't know if they fixed the thing where you could remove the holy status and then raze it anyway). I don't really see it as the same as stopping population growth by ticking the box.
At some stage of the mod you couldn't stop the razing once it started. It was a bug I think? But in some regard in this context it might have made sense. You either burn it now or keep it and then the burn button shouldn't be there anymore.
Normally when you get unhappy for one reason or another you have to build something, reshuffle specialists or get some kind of luxury (which may or may not help). Building something takes many turns; depending on game speed. Shuffling and getting a luxury could be instant. But unhappiness is normally a multi-turn issue you have to deal with. Here you could basically then decide that "oh you are unhappy .. time to die!" and burn off the excess pop at a rate of one per turn; so you probably don't have to run it more then a turn or two. Then everyone is super happy (or at least neutral) again. It would be the fastest way probably to fix unhappiness without much consequence. Which is a bit weird.
I seem to recall previous versions of the game where you could basically get rid of a city by starving it down and then building a settler and you would remove the city. Don't recall which version it was now since it was quite some time ago. I don't think I'm imaging that one.
There is also the issue if you had "resettling" how long it would take etc. How long does it take to dismantle your city. To plan it and to execute it. I would think it would take more then a turn considering how long it takes to build just a single building etc. So I don't see it as a quick fix happiness issue solver in that regard.
As for barbarian farming; raze to spawn them, when you get low pop you stop burning, let the regrow and burn again. Will it be worthwhile? Probably not really but it might be something to do with undesirable cities you want to eventually get rid off. You normally won't get XP from barbs after lv2 (or 45 xp) but you still get yields from them if you kill them (Orders, Authority, certain wonders etc). It's not a great amount but it adds up. Sort of like farming enemies in war but more controllable. But it's a playstyle thing in some regard. I am not much for keeping enemy cities if I don't have to. They usually get burned. During the wars down to like size 1 to keep the land and a healing zone and then when the war is done you burn them all and resettle the land.
As for this being some kind of exploitable scorched earth policy where you raze cities that are in the risk of falling to the enemies. I am not sure how viable that would be. It might in that regard depend on how long the process would take to complete. It's not like you could run the process X-1 turns and then just keep it in the one turn away from completing state like you could with a say a building (people that invest several turns into say walls but then don't complete it to save the maintenance until they need the defence ...).