Well, there are only so much that the colonial revolt nations can do. In fact... your screenshot.. that's the strongest AI USA and Mexico I've ever seen, if you started in 1444 and they spawned instead of starting in a later date where they already exist.
One thing is that the Europeans cannot recruit mercenaries in the New World (since it's distant overseas) that they need to rely on their own manpower recruitments, which can drain pretty quickly if they are also busy in the Old World. A revolter state can finance mercenaries in their home continent at will, so as long as the revolters reach a certain size, the battles are in favor of the colonial nations. But there's a limit to what they can do, because they cannot generate sufficient war score to demand anything except by 1 waiting for a long time for the wargoal ticking warscore to rise 2 invading the European mainland itself. #2 does not happen usually.
But that said, it's entirely situational if the revolt states succeed or not. As long as the colonizer keeps a healthy economy, low war exhaustion, decent stability, etc - anything that goes for low revolt risk - the colonial nations may never claim independence.. well, it's obvious humans are better at managing revolts, but AIs do just fine as long as they don't get caught in a weird spiral by long-ass wars in Europe.
One thing I noticed is that it may be better not to convert the native cultures in North America, like Shawnee, Creek and Cherokee. I didn't bother doing that in one game, and the USA revolted, which I promptly vassalized as soon as chance arose. Most of the Atlantic coast of the North America was owned by GB then, so USA's primary culture was English. I returned the USA cores and sold the rest of the non-cored but culturally English provinces, but the USA just wouldn't buy anything Cherokee, for example. USA was Protestant, I was Orthodox, and USA was willing to buy English-Orthodox but not Cherokee-Orthodox.
So... my guess.
I'll just make a blind assumption that the USA in the OP's screenshot spawned from GB, and GB conquered the natives. GB presumably converted the native cultures (which they often do, since it's cheap overseas). The USA, then, was more inclined to take those same-cultured provinces, and they would have had less desire if the area didn't belong to their culture. Well, it's just my conjecture. AIs do go for conquering people regardless of culture when they can.