I would not be so sure about the aspect of Suzerainty. I had quite a few examples, when a distant (to me) CS was living happily under the Suzerainty of a big neighbouring AI civ, and as soon as I overturned their Suzerainty there and made sure I stayed the Suzerain from that point on, the former Suzerain AI would just declare war on that CS before too long and take it or even raze it. It happened enough times for me to change my ways: nowadays I tend to take control only of those CS that I can defend, meaning those closer to me or with an easy access. If you take control of a distant CS that you can't easily defend, you just paint a big red target on it for the AI.
Overall, I find the aspects of AI aggressiveness towards city states quite realistic. AI is showing "tall players" their place in history

In the beginning they seek to have just another city in their empire, and the more cities, the better. Afterwards they seem to dislike if anyone upsets things in their spheres of influence: "if I can't have it, neither can you" - this is very plausible