assuming it goes undergoes the appropriate 'process', what is to prevent "Yesterday" by the Beatles from becoming a folksong?

Absolutely nothing. If all the radios, TVs, turntables, CD players and iPods in the world stopped working tomorrow, 40 years from now we'd have a fine crop of new folk songs, and I wouldn't be at all surprised if Yesterday was one of them. But that's the only way it - or any other song - is going to undergo the appropriate process now.