Good post. I had an organic chemistry prof back in the late eighties that remarked something like, "if you think the origin of life was some sort of random event, think again". This was a really bright guy no one would take for a religious sort.
I approve of this interpretation.
You don't converge when each next term is astronomically bigger than the previous one.
It appears, already, that amino acids and RNA were inevitable, and RNA turns out to suffice for the needed enzyme operations. RNA that replicates other RNA arises spontaneously. Once you get two of them, the seas fill with variations of everything they encounter.