It seems quite likely that this isn't actually fundamentally true, because the real story was a mess.

If you look at bacteria even, there's a lot of genetic transfer beyond just strict parent/child relationships either just directly or via viruses or other things I'm sure I've never heard of.

The earliest life was probably more like some kind of soup of self-replicating things, closer to a chemical reaction than biological, and then it would have been kind of a sliding scale over a long period of time before we get to anything that really looks that much like "<this> organism begat <that> organism".

The entire concept of organisms themselves are an abstraction over the truth, that kind of works for today's world, but probably less worked when things were new and interesting and messy.