>At that elevation at Mach‑5, air around the nose and leading edges can reach temperatures exceeding 1,000 degrees Celsius (1,832°F), a challenge...

It is not the conical nose or leading edges that are the show stopper problem(s). There the shockwave generally does not touch the craft. The internal shockwaves that touch the walls of the engine ducting are. The heat loading and heat soak ability on those shockwave impingement sites will limit the duration of hypersonic travel.

Hypersonic travel through the atmosphere is easy, a problem solved in the 1950s. Be conical and carry your oxygen internally. Hypersonic travel that is air-breathing is an entirely different class of problem and I don't think it is anywhere near to being solved.

The only silver lining is that at hypersonic speeds you don't need to be propulsive for very long to get anywhere.