I would say the approach here is based on scale. I have no references on this, I am exposing my educated guess.
I think there is a relation between the energy transfer and the relevant scale receiving this energy. That is how I would explain the difference between pushing a wood piece, with a rather slow movement, while a skilled martial artist is able to break it with a sudden movement.
This is also evident when observing a fan rotating and trying to shoot a paper ball between two blades: if you shoot at slow speeds, the fan behaves like a wall, impenetrable. This is because their movement is much faster and their average occupation of space is such that the probability of passage is small. Only at high speeds the penetration holes become apparent.
This in my mind is completely analogous to the collision between any two physical bodies. And the qualitative rule is: the collision is an energy transfer that occurs in a time interval and in a certain volume or area, which completely define the expected result. These time interval and volume area of interest are completely related to the relative momenta of the bodies.
You can throw a baseball to a window, and it won't break as long as the speed is low enough. Because at these speeds the whole window is involved in stopping the ball, the whole window receives the tension of the impact and that tension can distribute throughout the surface in the time scale involved.
For a faster throw, the ball will break the window, or cause fractures that go all along the surface, long lines of rupture. Here I would say that the energy transfer in the impact was so sudden (a smaller time scale than before) that portions of the window vibrated w.r.t to other in amplitudes which decoupled them. And probably the relevant scale here is represented by the average size of the pieces.
One can see that for even faster speeds, only a hole close to the size of the ball is left of the collision, where energy stayed in the pieces broken. Transfer was here faster than the transmission to other parts of the window, so fast that the other regions didn't notice.
In your answer I see an analog. Although in the quantum world particles cannot be localized, nor their momenta measured with the same precision, something analogous happens. It is well known that wavelength plays an important role in collisions. Neutrons of low energy can scatter on atoms much like balls, and the more their energy approaches the keV range, at which their wavelengths are comparable to nuclear scales, the more they excite the nuclear energy levels and get captured, where nuclear resonances appear in the spectra.
So in the case of electron, only at energies high enough, and wavelengths small enough could it interact with the quarks. This also means that the appropriate timescales became relevant at these energies, since quarks are supposed to have a large momenta distribution inside protons, and at lower speeds the interaction would be similar to the fan blades example.
