> It will take at least 30 years, probably more like 300. The danger is that we collectively take a more destructive course.
I don't think there is a clear trend toward this goal at all.
Extrapolating current trends, we are fairly likely to peak in total population as a species long we become space-constrained on earth; more remote living space is pretty cheap in basically every industrialized country right now, and living in a conventional house in the boonies is like ten orders of magnitude easier than making anything extraterrestrial work (neither climate change nor even global nuclear war is enough to flip that).
Sure, people might like the concept of space colonization, but we're not seeing significant amounts of people living on boats in the Atlantic, so I would not expect to see people living on spaceships within the next centuries, either...
Be careful to note that I didn't say the majority of people would be living in space colonies, but that the majority of inhabited land area would be found in them.
Probably you're right that most people will choose to die on the same planet they're born on. Most people today choose to die in the same city they were born in, and most coconuts sprout, if at all, within a few meters of the tree they fell from.
That doesn't mean that coconuts' ability to float across the ocean is inconsequential to coconut species distribution. It only takes one coconut making landfall on a barren atoll to start a new coconut grove.
There are, in fact, a significant number of people who live on boats. There would be many more if the boats weren't dependent on docking to refuel.
It's a mistake to extrapolate from current trends when it comes to exponentially growing phenomena. In April of 02020 covid had killed less than 1000 people after six months. In 01770 two million years of human beings had managed to speed up their transportation from the speed of a marathon runner to the speed of a racehorse. You have to look at the underlying dynamics, and even then what you often learn is that the future is very uncertain.