Naturally most of these differences are only apparent to players, not to listeners.
The desire for vintage instruments is rather like that of any obsessive collector: those not in the know will be totally bemused as to why a late 50s Strat should be worth (say) 20 times more than a modern copy. And maybe a 100 times more if someone famous once owned it.
Of course there is rarity value, which dictates the price of any antique, regardless of its use value.
And there are some very subtle differences in sound between vintage instruments and modern ones - and not ones which might appear wholly good.
I once played a friend's 1964 Strat, and compared it with a modern Squier Strat. There was certainly a difference in sound: the older one had a kind of grittiness, a "worn" quality. Rather like the difference between a well-worn leather jacket and a brand new one. (And who wouldn't prefer to be seen in the former? Only a terminally uncool person...)
Guitar experts will say that's because the pickups on the older models were handwound, which resulted in more random construction than the "perfect" later machine-wound ones. So the early models have a kind of "character" that newer mass-produced ones don't. From one angle, that's an "imperfection". But it's the same kind of "imperfection" that makes some people prefer vinyl to CDs, which are theoretically more accurate.
However, this is still something that only the most discerning player will spot. Audiences don't give a damn.
I own an early 1960s Epiphone Casino (built in the Gibson factory in Kalamazoo). In many ways it's an inferior guitar: it goes out of tune more than my 70s Tele, and probably more than a modern Casino (made in Japan) would. But the tone (largely down to the P90 pickups) is to die for - IMHO. The sound of that guitar through a genuine valve amp (especially a 60s valve amp) is a kind of holy grail. You just know it's "right" when you hear it (the kind of fruity sound old 50s and 60s records have, that you just can't get today). It's not nostalgia, it's real.
I do think an untrained listener could spot the difference from a modern equivalent - but of course they'd probably be hard pushed to care!
IOW, the difference may not be down to nostalgic delusion, but caring about the difference probably is!