Getting them angry is not the same as getting them to declare war.
No, it's just a heckuva good move in that direction.
The AI usually also hate each other, so if their relation to you has a big difference on how likely they are to declare war (I believe we don't know the exact mechanics yet), your actions to annoy them only makes you another possible war target. I've played several games where most AI are denouncing me all the time (with good reason) but nobody ever declared war.
The mechanisms don't seem to be that mysterious. Appearance of Weakness can get you War and Late-Game Victory Chase can get you War, and pissing off the AI with more negative diplomacy modifiers seals the deal.
Yes this was basically the point I was trying to make. The computer shouldn't declare war unless it thinks it can get something from it. CiV toward the end did a better job with this. Civ6 is a bit sad right now, but I'm confident someone will fix it.
Now, if we want to talk about sticky issues, what can be gotten out of war (or peace, for that matter) has plagued all 4X games. It's usually a big drain on time and resources, and a diversion away from building upon existing assets for something that can be a big gamble. In both Civ V and VI, terrain is fairly ubiquitous, so there are no particularly covetable stretches of land, although the AI does want to settle on luxes (and frequently simply won't expand in their absence). On the other hand, the AI doesn't seem to place a high value on having a peaceful place to send trade routes, so peace isn't that coveted either. Add into that the dichotomy that devs know all too well: players get angry when an AI is rabidly aggressive, and disappointed when it's not aggressive enough.....Catch-22.
But if players really want war and they're not getting it, then there's a good chance they're not trying enough of the stuff I mentioned previously. Dance some units around their border, then break the promise to stop doing that. Settle near them, then break the promise not to do it again. Convert a city, then break the promise not to do that again. Spy on them, then....well, you get the idea. Do all that while keeping your military strength from getting too high. Oh, and I guess you need to avoid the lower difficulty levels, where the AI is anemic to war.
TLDR: There's a good reason for getting a warmonger hit for taking cities, even if you didn't start it. It can be gamed. Even now in VI, people game the lack of warmonger penalties to capture cities by just building a small force of archers and some token infantry, then letting the much bigger AI army come over and pick a fight because they perceive themselves as stronger. They lose their army in a failed siege, and their capital is ripe for the taking.