Although it may seem safe to assume that one horsepower is the output a horse is capable of creating at any one time, that is incorrect. In fact, the maximum output of a horse can be up to 15 horsepower,[2] and the maximum output of a human is a bit more than a single horsepower. For extreme athletes, this output can be even higher with Tour de France riders outputting around 1.2 horsepower for around 15 seconds, and just under 0.9 horsepower for a minute.[3] https://energyeducation.ca/encyclopedia/Horsepower
I must now once again question the nature of reality.
the maximum output of a horse can be up to 15 horsepower,
That's the problem. The unit was not developed on the maximum power a horse could put out. It was intended to be what a typical horse could continuously sustain throughout the work day.
Also why switching horses was a thing: a fully rested horse could run at a higher hp, then change horses and the new one could keep outputting thevhigher up whilecthe previous one rested.
Like switching rechargeable batteries, only the battery was the horse.
It's just playing with fractions and linear extrapolation. Horsepower has a time denominator. If you measure how fast I can run (not fast) in .1 second intervals, then take the highest number and extrapolate that to miles per hour it will seem impressive.