“That would be the equivalent.”
I don’t think it is equivalent, because there was no one group in 1915 that was ever as big as the Beatles. Also, the Beatles continue to be fairly prominent culturally to this day, with their music still being used in movie soundtracks, commercials, etc.
1915 was not a fair comparison
How would a group get huge with no radio? People were still buying sheet music for home entertainment!
In those days when radio and the recording industry were just getting started, you didn't have popular recording groups in the same way you did later.
Probably the equivalent would be a successful songwriter like Irving Berlin. I suppose 60s kids did have an inkling of who Irving Berlin was -- more from the movies and Christmas songs than from his earliest tunes -- but they probably didn't much care.
Of two alternatives -- everybody being fixated on the popular culture of 60 years back or young people never learning who Paul McCartney was -- the latter may actually be better. The problem is that they also never learn some things that are a lot more important.