The resonance gets weaker the more closer to the headstock, just stum the guitar and touch the headstock and then body-quickly one can realize there lots more resonance (rumble) on the first frets compared to the body.
Funny actually we change or modify bridges for tone but usually forget there is also another end of the string
So I guess the main concern with neck thru is to eliminate this as much as you can by "sharing" the resonance through body and neck.
One solution is if you don't have a nack-thru but want the tone is the place weight on headstock, similar to idea of brass block upgrade used on floydrose trem.s.
The link shared a picture where satriani used something like that. A brass plate can be cut to shape of headstock so this upgrade can be almost invisible.
The solution to the problem of a resonant headstock is a volute on the neck to stiffen the transition point from nut to headstock. Manufacturing takes a lot of wood away from that area to insteall the nut, the screws for the nut, and the truss rod.
This is a major reason products like the Groove Tubes Fat Finger get mixed reviews. They work great on a strat or a Tele, because the headstock isn't angled and isn't a seperate piece of wood, on top of not having a volute and the distribution of force is changed by the string trees.
On guitars that have properly designed headstocks, with a volute and a decent break angle on the strings, very much less energy is actually transferred into the headstock and so a Fat Finger doesn't work anywhere near as effectively, because it counteracts resonance by adding mass (And thus you end up with the same amount of energy in the string, trying to move a larger mass in the headstock, and basic physics tells us this is more difficult than moving less mass. The result is less headstock movement, and that energy has to go somewhere, so it simply remains in the string, where it can be reliably converted into kinetic energy through vibration)
So yes, making a headstock larger can improve sustain. But not because thats the technically correct way to improve sustain. More can be achieved, and more reliably, with less variance from different pieces of wood, by simply designing properly.
(This is also a reason I don't like a lot of ibanez necks. Wizards with no volute don't just fit my hand badly, they rob sustain since there's an absolute minimum of material at the weakest point of the guitar neck, and that means bad **** goes down in terms of reliability, tone, and sustain. For some shredders, thats no big deal because it can be counteracted by using a metric ****ton of gain, which compresses the sound and makes it sustain longer at a given level.)
As far as neck through goes, the principle is that if you have one piece of wood, there are no glue joints or screws through which energy can be dissipated unnecessarily, and thus we remove another possible point through which our vibrating string can be robbed of vibration. Its nothing to do with feeding resonance "back" into a string, and everything to do with making sure the energy stays where it should be in the first place.