and the Condorcet method can completely fail to select a winner.

That one’s not a flaw. All elections can suffer from ties. Pure Condorcet just makes it obvious when there’s a tie (and this is very rare). There are a bunch of Condorcet completion methods for resolving the tie.

Unfortunately the form of RCV used everywhere in the US is Hare’s method, which eliminates candidates based only on voters’ first-choice rankings, which largely just perpetuates all the same problems as FPTP. There are many other better reforms. One of those should become the norm instead.