I always thought the problem was intractable and related to just ... moving through the atmosphere at that speed induces a lot of drag. Has there been any sort of major breakthrough that would change that?

I guess you could always fly at a much higher altitude (with its own problems) but it all seems motivated by, well, prestige as you put it. Like, I have a hard time believing it'll ever be more economical (as a commodity/for the market), environmentally friendly, profitable (for the operator), or just more practical than transsonic flight. The only advantage seems to be bragging rights, and the ability to cross great distances really quickly for an elite few.