Earlier quoted context omitted.
If it's an aviation engine, it'd better be able to!
Multiple thousand at max power? Typically, overhaul at 2000 hours. And maximum continous power isn't usually full load.
Our flying club engines in the 172s typically make at least 3000, if not 3500 hours, and I think some of the overhauls at that point have been a "Well... it's still perfectly fine... but..." thing where the board was just starting to get uncomfortable with the hours on it.
And, yes, they spend a lot of time making less than rated power, because of density altitude, but they're still rated for full power operation, and since there's basically no wear going on with an engine in operation (almost all the wear is during starting), there's no real difference there.
It's not until you get into the really large engines where "maximum continuous" is a different thing from "takeoff power." The turbocharged 500s are about the smallest I know of with that sort of rating, and even then I don't think it's all of them. Most of the big radials have that limit, though. If you find a smaller plane with that sort of limit, it's either a possible resonance issue between the engine and prop, or a noise regulation for certification.