In order for any polymer to gain a selective advantage over any other polymer it must be a template for its own replication. Proteins as polymers do not provide a template for own synthesis . DNA, RNA or something else as the original self polymer . Problem with DNA Lacks any catalytic properties. Ability to catalyze a reaction gives it a selective advantage.
Nucleotides are hard to make.
5' phosphates hard to make. RNA as the original biopolymer Ability to self replicate. Ability to perform catalytic functions. Ability to catalyze peptidyl transfer. 2'-OH is very reactive, causing degradation of polymer.