If you have the money to live in space, you have the money to live "your way" on Earth unless your way is odious enough that other people will actively intervene to stop you.
Sorry, that's unrealistic. The current status quo is not so flexible to allow any and all types of governance even if they aren't all 'that' odious. Quite a lot of ways of doing things are illegal for the one or other reason.
Attempts by the various rich to change that don't always really work to well, as there are always lots of other rich that want it the other way, or yet a third way. Thus leading to a continuous competition and obviously many losers even among the people with 'that' amount of money.
Or in other words, no they can't. There are a lot of people who can not get what they want even with that amount of money.
Secondly, some people do want such odious ways, so obviously they clearly do want to go.
As such you appear to be making a special pleading, that requires all humans to be willing to work in the system, even though there are quite a few humans who don't. And we know they exist from the occasional sea steading and space colony ideas they push. As well as that this was a motivation of early colonists in the old days, off to create their 'utopia'. Or even the attempted coups now and then, in each of those there are winning and losing sides after all, and in the past when it was still possible, the losers would then at times go off to found new colonies/countries.
This is factual human behavior, so I'd want some evidence on why suddenly they wouldn't now, even when in the pats they would at considerable hardship.
Terraforming is even more of a dead letter than space habitats. A species with enough resources to waste on it doesn't need another planet. It is a hugely expensive, centuries long process that requires many generations selflessly devote resources to something they, nor their children, nor their children's children's children will ever see the fruits of. It makes total sense if you are playing an RTS and your goal is maximum territory, but it makes little sense from any individual human point of view.
This is a weak argument. It doesn't matter if most humans are like that. Even a few exceptions with sufficient wealth each generation will do. (ie Elon Musk)
Secondly, it doesn't need to be an individual, even if individuals are short term thinkers, governments have at times been willing to make long term investments over many generations if it will eventually benefit the country. For instance for a modern example The Netherlands ran a multi-generation project for reclaiming land from the sea, doing each step as they could afford it, for the betterment of the country long term.
Lastly, I didn't say humans would do this (rather I suggested humans were more factional), I said an alien species with a tendency to long term thinking might... heck, what if they live a thousand years? Then it might be done in their life time at that.
Each of those reasons on its own already mean your argument appears to weak to be considered a sufficiently strong argument to hold, let alone all three of them together.
As such, not only does it totally make sense in an RTS, it apparently also makes sense to some people and governments in real life. As in, it makes so much sense they put billions in to actually doing it.
So unless you have facts showing this is all a mirage, I think it would be hard to accept your position that all of humanity are short term thinkers only here. It just doesn't seem to match reality.