Why do they assume that a proton is spherical?
Because they’re physicists. Don’t you know the joke about a physicist designing a dog house? “Well, first we assumed the dog was a sphere...”
(By the way, even ellipses and prolate and oblate spheroids have radii.)
The shape of a proton depends on the speed of the quarks inside. The spherical shape is the shape most physicists expected to find. The peanut shape is produced by quarks traveling nearly at light speed and spinning the same direction as the proton.
Better yet: why do they assume that the proton, as particle, has fixed physical dimensions? As a wave, its dimensions are zilch; as a particle, I’d expect them to fluctuate. Perhaps this 4% deficit is actually the “lower bound” measurement.
Actually, I don’t think they do. But the amount of space it takes up is spherical because it moves at high speed. It’s actually a wave. If that doesn’t make sense to you, it’s because it shouldn’t. Any attempt to relate the nature of subatomic particles is pure metaphor, and I’d be lying if I told you I understood it.
Why do people believe the Earth is round?
It’s a quantum particle, it can be any shape you want it to be.