Usain Bolt topped out at like 29 mph, and (I don't have my numbers with me) had a ridiculous speed for 2 "rounds". I think his performance should be doable by an 8th level character who spent both of their ASIs on feats, and maaaaaaaaaaaybe is utilizing something like Cunning action to get extra movement (I don't like having to make every athlete a rogue or a monk to get double dash, I actually don't like double dashing and think cunning action is about doing two things at once so double dashing shouldn't be there ... that's a different thread). But 29 mph requires like 300 movement and with a base speed of 30, +10 for a feat still requires a x7 multiplier for running and that's really high.
High level non-casters should be able to do mythic/tall tales level feats of ridiculousness. I don't think only spells should do fun stuff.
Other than sprinting speed, what's probably more applicable to adventuring is long distance jogging. Aragorn, Gimli, and Legolas ran for how long? Humans can hold a double move (6 mph) for a really, really, really long time when they're fit.