Proxima is flare star, massive stellar winds would outstrip any atmosphere, habitable zone is on approximately 11d orbital period, more x-rays than sun, etc...
On earth, much of it as I understand is because the “good land” may already be occupied by others, and (initially) less competition in a new place may make it overall less inhospitable than surviving in a fertile but competitive land. After initial generations settle there, future generations will often stay in their native homelands by default unless driven out by other factors. Of course, this is just reasons for settling around Earth itself; who knows what drives the motivations of alien species?