As you say, one major problem was that the aircraft skin got really hot from friction - hot enough that they had to build it out of a special titanium alloy, and paint it with heat resistant paint - but that was inadequate. Due to the heating and cooling that occurred each cycle the entire airframe would expand and contract very substantially - over repeat cycles this lead to metal fatigue, and would lead to failure but not for incessant expensive maintenance. For an idea of how much the thing expands, on the final flight of the model now at RNAS Yeovilton, the flight engineer stuck his cap between the engineering console and the bulkhead, where it remains sandwiched by pressure today.
Apart from the thermal issues, the entire craft suffered from “so cutting edge it barely works” all over, from special tyre compounds to window seals to the famous drop nose. It was an engineering marvel and nightmare, in one improbable package. It’s frankly surprising it even ever existed.
I think the major difference will be that Concorde was a space age plane built with 60’s tech, and these will Be space age planes built with space age tech.