...Then again, other, far mightier civilizations are known to have fallen when their capital worlds did (Tkon, Iconians). Perhaps there exists a socio-econo-political mechanism for that, one the UFP is not immune to?
I think the destruction of those Empires may have begun with the loss of their Homeworlds, but it wasn't the single loss that destroyed everything.
Honestly, I did think it was silly how there was only one major Starfleet Academy/HQ and it had to be on Earth. It wouldn't surprise me if there were secondary locations on the other Founding Worlds (Andor, most likely) and we just only ever hear about the Earth ones.
There are for NCO's and crewmen IIRC
One would like to think that a non-martial empire like Federation could survive fall of Earth, although it would be significantly weaker. But I wonder if there are significant cultural and political differences between diverse member worlds or if they are all pretty much tightly knit and fanatically loyal to the ideals of the Federation?
On the other hand, if Romulus or Qo'nos fell, I have no doubt that the two empires would immediatelly collapse, or shortly after when somebody invaded them while they were weak. Think of what would happen to Roman empire if Hannibal had conquered Rome?