Oops, I think you touched on something else though that I missed also. If the string's enery is moving the top to make sound it would die sooner.
I.e. except for using acoustic feedback', we use solid bed guitars for more sustain.
Thats probably the greatest factor at play. The soundbaord and the body enclosure is a remarkably good system for what it does, but along side the sensitivity of a magnetic pickup it's not very efficient. Think of it this way. A plucked string has a given amount of energy in it as it vibrates. The way that energy is lost is the key factor. Ignoring the thousands of subtle things that go to make up a nice sounding instrument the essential thing common to all is where and how is that energy lost or transfered into soundwaves.
Two systems Acoustic and Electric.
Acoustic. The energy in the string is mostly lost in these ways.
via the air as soundwaves directly off the string.
via the nut and headstock as energy is transfered to the wood.
via internal damping in the mechanics of the string. The string material will be self damping to a degree. It's own impedance.
via the bridge and onto the soundboard and it is this part we hear.
A good deal of the energy of the string is reflected back down the string at the nut and the bridge/saddles. It is this that gives us the relationship between amplitude and decay or in simple terms volume and sustain. They are essentially related. More volume = less sustain and vice versa.
Electric. The first three still apply but as there is no soundboard or enclosure a good deal more energy is reflected back down the string, this will effect the decay or sustain and as you'd expect the acoustic amplitude or volume is much less. That allows for the pickup to keep detecting the vibrations in the string and convert them into an electrical signal related directly to the amount of string movement and the frequency. That signal is then amplified electronically rather than via a soundboard and air enclosure.
Completely different ways of generating audible sound waves. Both are fantastically complex in reality but very simple in the basic theory.