Here is my theory:
I believe that because exorbitant licensing fees has made the music of The Beatles virtually unrepresented in film and TV, their songs retain a corporeal presence that most big hits of the era have lost.
The Rolling Stones's "Satisfaction," for example, doesn't quite feel like it's of this world anymore, does it? It belongs to movies, it's the Apocalypse Now song, a song that has a narrative meaning outside of our lives. The same with "Sympathy for the Devil" and "Layla" and "Run Through the Jungle." They're songs that aren't defined by our relationship with them, but the relationship fictional characters and some vague sense of Popular Culture have with them.
Just look at "All Along the Watchtower." It's as strong as song as any ever written, but there's hardly anyone who hears it in any setting without immediately feeling like they're in the codified television version of the 1960s, or, depending on your version, outer space. It doesn't belong to this world, it belongs to The Culture. Nobody hears it on its own terms anymore.
The Beatles don't really have this problem. "A Hard Day's Night," maybe, immediately conjures up black and white swinging London, and "Yellow Submarine"'ll put you in the headspace of a stoned cartoon, and the Joe Cocker version of "With a Little Help from My Friends" is nostalgia incarnate, but other than those, the works of The Beatles are a blank slate that we interact with on our terms and on the terms of the music itself.
"Hey Jude," "Taxman," "Dig A Pony," and so forth are inescapable radio fixtures that we've all heard a buhjillion times, but because they're almost completely absent in our narrative entertainment, they're still ours.