We do have ideas! Specifically, within the RNA world hypothesis, the transition period is called the virus world [0]
> given all the incredibly, insanely, unbelievably rare DNA sequences that exist in the world today,
We have a good understanding of where diversity comes from, I'm not sure what point you're making here.
> why is such a fundamental process not abundant as fuck already. Where'd it go? Why is this even a mystery?
I don't think anyone thinks this process need be 'fundemental', though it definitely is pivotal. It only really needed to happen once, and then DNA was off reproducing and spreading by itself. That said, it looks like viruses converting RNA to DNA could still be happening today.
In general, we don't expect novel self-reproducing molecules to arise today, because they are out-competed by existing self-replicating molecules. In a world where nothing is replicating the first replicator is king. In today's world a brand new replicator is food for something else.
> Maybe it's possible that your romantic view of how this all happens (pseudo-Darwinian circa 2020) isn't telling the whole story?
I don't think I, or anyone else really, is claiming to tell the whole story - just that we have good reason to believe this came about through physical processes, and no evidence to believe... well I'm not sure what else there could be.
What are you proposing?
[0] https://en.wikipedia.org/wiki/RNA_world#Evolution_of_DNA