Clearly all the dna of eukaryotes is so related that it cannot be due to chance. But could it be that archae and bacteria formed from separate abiogenesis events?

Or could eukaryotes have formed multiple times? We know that encapsulation of bacteria to form organelles has occurred at least twice, namely for mitochondria and for chloroplasts. Could it be that different eukaryotic kingdoms have mitochondria that are not related?

>If the conditions necessary to spawn life essentially produced a population, rather than an individual, then I don't know that we'd be able to tell the difference without seeing it in action.

Yes this is essentially what I meant, the question whether all life comes from one single cell, of if at some point the conditions were such that many cells formed that were very similar, maybe even with similar dna that was being copied, floating around.