we could colonize the entire galaxy in 200 million years
This is just extrapolating based on math, while ignoring the reality of the actual situation.
Even if we have an amazing breakthrough tomorrow, the reality of interstellar colonization is that you would necessarily be creating two different species by doing so. They would have very little reason to cooperate after a relatively short time. Space is huge, y’all. Communication would be cumbersome at first, and rapidly get worse as the two different species diverged, first culturally, then physically.
And that’s even assuming that we would do it. You’re basically asking a large group of people to sacrifice enormously for, at best, a marginal benefit. We can’t even convince people to stop burning coal, and that’s for our own enormous benifit.