That's quite a jump in time scale. The overall lifetime of the human species is miniscule, relative to the timing of mass extinctions.

Of course. But once we are immortal, the timescale changes.

Fair enough :)

But on that scale, why would we be limited to flesh? I'm reminded of Sobornost practices in Hannu Rajaniemi's Jean le Flambeur trilogy. Basically, make numerous copies of a mind, introducing more-or-less random changes, and select on some set of criteria. I mean, why is natural selection limited to biological systems?

It's not. We could in the end create our own pool for it. Would we be wise enough to do it?

Well, if a few billion people were doing it, at least some of them would get useful results. We might get lots of [insert name of "famous" person] variants, however.