It's not about habitats coexisting with each other or not, it's about them imploding internally because people develop factions, compete for resources internally, threaten brinkmanship with critical systems, and eventually someone goes too far -- like people do all the time in countries all around the globe today.
Except a company can go bankrupt and a political regime can be replaced without all their employees or citizens dying in the process, because none of them are responsible for maintaining earth's life support.
But not all of them. And the ones that survive have the opportunity to learn from the ones that didn't.
That's less different from Earth than you may think. We've witnessed entire countries collapsing even in the last few years. If it wasn't for Earth providing free air, reasonably cheap water, and not-that-difficult food even when your local political system collapses, nobody on Earth would even consider switching their country to run on Communism; rather than merely killing dozens of millions of people it would be witnessed as bringing total extinction to anyone who tried it.
Basically, evolution doesn't stop.
You don't need "a system" for doing this. You only need one. 9,999 of 10,000 habitats could be staring into their naval, but the one building more will still be building more. So, I think you ought to flip the intuition around; it's not a question of keeping everyone on board, it's a question of what it takes to extinguish everyone's ability to do this, which, once it gets going, would basically amount to "a local supernova".
"I have even the remotest faith we could manage space habitats politically"
Again, I think maybe you're envisioning a world in which all the space habitats are just peacefully co-existing... but this is not a necessary precondition for them to exist, or propagate. Yes, they'll war, and they'll split, and they'll join into groups, and there will be diversity that makes the current diversity on Earth look like boring homogeneity, because there won't be such a strong force pulling people back towards a single species mean. It doesn't have to be utopia to exist.