Considering the same pressures are behind space colonization as were behind colonization of old, I find your concerns as merely speculation based in fantasy and not history.
> but what if "here" is the problem?
The same "here" that is humanity's proverbial garden of Eden? Food grows out of the ground, an atmosphere can exist and it's breathable and, until relatively recently, we didn't have to worry too much about the Sun's radiation destroying our own biological processes.
If "here" is the problem, and the solution is a dry, cold rock that's millions of miles away without any signs of life, we're truly doomed.
> If the Pilgrims had stayed in England and the Netherlands, they wouldn't have been able to fix what they considered to be "the problem" no matter how hard they tried
The problems pilgrims face were those of religious persecution. The problems we face as whole are truly existential, we're in the process of changing our planet for the worse.
The same forces that are driving the destruction of our planet are driving space colonization. I don't see any evidence to the contrary.