I think there are bout 5 directions we are looking at this
and that seems to be the problem
first, let us look at how a pickup works both electrically and mechanically
A pickup is mechanically a magnet(s) and a electrical coil, the magnet or pole pieces, shape a electrical field that when disturbed creates a electrical chrge in the coil
Faradays law of Induction
That law, is valid in the pickup not generating any charge (noise) if the magnetic field is not disturbed, the only way that field is not disturbed is if their is not any ferromagnetic forces exerted on the field so it is stable.
Moving the strings which are ferromagnetic or the pickup around the strings will cause a signal. We do not want sounds not from the strings, we want to pick up the harmonics set up from the strings.
A simple experiment would be to screw a pickup to a board and swing a metal object over it. when we hook up a meter to the pickup we see it is effected, now we lay the metal object on the board and swing the pickup, we see the same reading on the meter, If we mount the pickup on springs and swing the metal object while having a drummer play a beat on the board,we see the meter give us a different reading than the first reading, as now we have more vibration.
so we have established that it is not how the disturbance is generated, but it is the disturbance itself that creates the signal. In other words a vibrating pickup will generate sound by itself if a string is near it. any vibration will disturb the magnetic field and cause signal which we turn to sound in the amp.
Now, we need to go to mechanical theory to see how a string effects the magnetic field, we need to see the harmonic vibration of the string, we go into a study of Node/antinode.
and how that is effected by the fret you are holding the string behind. We also have to look at the speed of the vibration and the planes of the vibration. Yes guitar strings vibrate on multiple planes. These forces effect the signal generated. To complicate maters we have the forces of the magnetic field wanting to pull on the strings. Ferromagnetic strings are pulled on by the magnets we are using to create the field and in this dampen the string vibration so we need to be able to adjust the distance of the stings from the poles of the magnets, and there is a entire study in this and that is for another day., That is though, why most pickups are mounted as they are, not for the sound, but so they can be adjusted for best compromise. And even when they are adjusted, if the pickup has individual adjustable poles we can further tune it for the harmonics of the individual strings above them.
mechanically there is plenty of arguments for different mountings, and they are all compromises as seen in the last paragraph, Springs vibrate and create their own problems, foam compresses and has memory not wanting to expand out how it once was, surgical rubber breaks down with environmental forces like oils from your hands. If only one was the answer then we would all agree on it.
Then there is the effect of hardware and wood, we want the string to vibrate in a natural harmonic to create as pure of a musical signal as it can, any other forces on the pickup create junk. We need the hardware to be solid, with out movement, and have no dampening forces. That is why one style bridge can effect the tone the same as cheap bridges. the mechanical joint in the neck needs to be as solid as possible or it is absorbing vibration,
Woods all have tonal differences and these are because how dense the wood is and how it absorbs the vibration of the string.
Etc Etc Etc. We could discuss the thickness of a pickguard, the fingers vs plectrum, slide Vs fret, capos, and on but it gets redundant.
let us not forget personal style, we all use different techniques to dampen strings and voiding unwanted noise.
Now, how much each effects the sound, output power, and junk noise of the guitar is something that can be argued for years as every ones ear is developed differently. But I think I covered enough bases here to see that the more stable of a magnetic field we set up, the quieter the guitar will be (let us discuss 60 cycle hum later guys) and if we could create the perfect situation then it would not be a guitar.