Extinction is common on Earth. Humans are the only survivors of the human simian branch. The difference there is as you mentioned: we have fossil evidence of the other lines. There is no evidence of non-LUCA lines. Still, an absence of evidence isn't evidence of absence. If we could understand why inert materials became alive, it would help understand why LUCA is the survivor if it wasn't alone.
As for "being told", Galileo found out the hard way that "being told" one thing isn't always true.
Agreed on Occam's Razor. Life appears to be exceedingly rare in the Universe. It would be remarkable if life arose more than once on Earth.
Extinction of select species is common.
But the genetic heritage of LUCA lived on in the species that survive mass extinctions, and is passed down the evolutionary tree by speciation, and modification with descent.
I agree there is nothing wrong with speculating about long disappeared lines of biology.
The problem with Galileo is he only had a hypothesis which wasn't strong enough to overturn existing accepted hypotheses, and he couldn't explain away the absence of stellar parallax if his hypothesis was true. Also, since we didn't know about the laws of inertia until Newton, Galileo's hypothesis didn't make sense from a motion and mechanics point of view