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My take is that people confuse the objective sound, which is almost entirely down to pickups and circuitry with the feel when holding and playing an instrument (which is a far more complex thing with woods and chambers and shapes and profiles and, god knows, maybe fret material, all giving an instrument a feel and character).
No one can tell from a recording whether a strat is poplar or alder, or with a maple or rosewood neck. IIRC there are arguments as to whether jimmy page was using a tele or an lp on some of the led zep recordings.
I think the whole point is that as long as the nut and bridge are rigidly separated then what is separating them isn't that important in terms of tone (certainly compared to pickup position) the strings have a node at each end and the movement of the string relative to the pickup creates the signal. For hollow-bodies it may be more complex inasmuch as the brigde may not be purely a node and energy that the string puts into the body as a result may be returned to the string later.