My Dad restored a 40 Ford in 1978 and had to (chose to?) rummage through dealers looking for new old stock, flea markets, Hemmings mail order for what he needed. (Some of what he wanted had "Ford" script on it for those originality points.) For a comparable 1971 domestic vehicle, now, I could get a crate engine and rebuilt tranny at Autozone...
Internet trumps all. There are private parties and junkyards that break cars into little tiny pieces, warehousing and selling them for peanuts on ebay. They then crush the body for the metal $$$.
I have no problems getting wear parts for my 27 year old Yamaha motorcycle online. The local dealer is a schmuck and has to order stuff.
The biggest issue IMO would be year-specific computers, coil on plug doodads, that sort of thing... which are small enough and promising (in $$) enough that folks would shelve spares indoors.
One may have to settle for rebuilt parts, off-brand, used, off-shore... but could keep a vehicle on the road as long as the body held out, for sure.