In fact, TIME's 100 People of the Century, in the "Artists and
Entertainers" category, included the following musicians and "musicians":

   Igor Stravinsky
   Louis Armstrong
   Rodgers and Hammerstein
   Frank Sinatra
   The Beatles
   Bob Dylan
   Aretha Franklin

That breaks down to one classical composer, one jazz innovator, two
representatives of the popular styles of the pre-rock era and three
representatives of the rock era.

To be fair, TIME also gave "honorable mention" to "runners-up" in all
fields, and I know Miles Davis at least made that "cut".

The whole exercise is rather questionable, though, especially since Bart
Simpson is one of the "people of the century".

As far as John Lennon's place, I've been thinking that in fact it is
Paul McCartney who is one of the great talents of the era.  His work
still speaks volumes even thirty years later, in musical construction,
songwriting elegance, and compassionate wisdom.  Before you jump all over
me as a hopeless boomer, let me observe that I can think of virtually no
other rock musician who has achieved that; McCartney's work, more than
Lennon's, Townshend's, or Hendrix's, has transcended the rock style to
an extent that none of the others named can hope to.

(Which is not to say that his efforts at writing straight classical are
worth anything, or that his post-Beatles solo efforts represent anything
near the peak of his potential.  But his best work possesses a maturity and
fully integrated awareness of earlier styles that is missing from most rock
artists.)

Personally, I see Shostakovich as the classical composer of the century,
and John Coltrane as the jazz artist of the century, but that's just me.

 - seb