But why assume a leap directly to proteins, by definition a long chain of amino acids? Couldn't we have started with self-replicating peptides and incremental improvements?
Peptides are just short proteins, and no, we have no idea how to get them either (though it's obviously easier).
Also, it's not that what I've called bad/garbage DNA doesn't produce proteins, it's that the proteins produced are useless: they don't "do" anything. There's no obvious reason why DNA "extension" should produce useful proteins over un-useful ones, at least, no mechanism that we have discovered so far.
Instead of accepting a theory of incremental improvement that "sounds nice", waving our arms about random chance and an old, vast Universe and going "yup, that's how it happened!", let's try to develop testable mechanisms and validate them.
I'm asking for more rigor while simultaneously shooting down "random chance", "plenty of time", and hand waving about the Law of Large Numbers. We've done the math and we need far more effective, directed mechanisms than random chance to produce useful DNA sequences.
