Just to give you an example, THIS is the kind of city/civ you guys are insisting is going to be a big problem to mad as far winning culture as a vassal: (note: spoiler from his RPC):
Tell me how that's a threat in any, way, shape or form.
Now, as to the reasons for taking a vassal vs just wiping a civ out:
1. Vassals bordering other civs enter the "land target" mechanics and allow for chain capitulations. Just ask danf how truly broken/stupid the way the AI evaluates capitulation is. Here's a few fun examples from actual gameplay that work just as fireaxis intended:
- AI has a 1 tile island city and you don't feel like taking it. Because you took that guy as a vassal, the opponent you're currently fighting won't vassal because his power is greater than all civ's average power...due to that 1 tile island civ that's already part of you technically. Were you to go into worldbuilder and do nothing but DELETE that vassal, NOW the target capitulates. So yes, you get weaker and they capitulate essentially. Note that this check doesn't care how bad you're owning the target, as long as its power is still above the average...
- When considering its own power, target counts its vassals. When considering yours, it does not count your vassals.
- I'm virtually certain there's something bugged about colonies and vassals. I've ripped the target so hard that there is absolutely no way it had above average power, and I had 4 times its power literally. If it has a colony, no dice.
- That said if you're at war with someone and someone who borders them is also at war, this is counted. Even if it's just a crappy 2 city vassal that otherwise hurts your cause, should this vassal be bordering target civ, then it still speeds the capitulation.....and a lot. This also works with any civ and war though.
- They only count for 1/2 land and pop. Assuming you ruin its chances of victory, a vassal can hold land for you and you can ignore it. It can't attack you, it won't trade meaningful techs with other AIs since its tech rate is left for dead. Essentially this allows you to control what more of the map is doing. If the objective is time crushing the world tech rate by damaging civs badly and taking them as vassals can/will work.
Ultimately, the biggest consideration in this particular RPC is how useful the cities will be captured. But, if they're just going to be razed or put you over the domination limit, there's no reason not to make use of vassals if you know what you're doing.