Why does the genetic nature of the polymer as a record of its function need to be the primary purpose for the original ancient life-like polymer? You identify

Why does the genetic nature of the polymer as a record of its function need to be the primary purpose for the original ancient life-like polymer? You identify the prion as a good candidate, but it's just a polymer that can do some sort of reaction (change the shape of another protein). By that score RNA is pretty great. We know it can do chemistry, and that might have been its primary purpose at first. It's possible that only later did the fact that it could store genetic information in the way we understand it today become useful. We have at least some evidence to believe that RNA was the first "living" molecule in that arguably the most primitive enzymes we have (ribosomes) are an RNA-protein hybrid, with some evidence to suggest the RNA was there first and protein bits were added/swapped out to make it better. It's also possible that a slightly simpler version of RNA was first and that the more complex bases came later. But all of these polymer monomers existed in the primordial soup, I don't understand why a protein polymer would be more likely to arise than an phospho-sugar one. Indeed the basic unit of energy inside pretty much all cells is ATP (one of the monomers in RNA), another sign that early life was very closely tied to phospho-sugar monomers.