I would be tempted to say that really great songwriters write songs that can be sung and enjoyed by almost everyone. ('Where have all the Flowers Gone', 'Both Sides Now', 'Rose Of Allendale'; songs that
my friends and I sang in the past still love to play)

(I'm as tempted to say that some songwriters write songs that are great by virtue of songwriter's performance (Dylan's "Thunder On the Mountain", seems to break some of the principals
of 'economy of lyrics', focus, etc., but for me it's addictive because of that voice).
Not something I'll be performing anytime soon, tho.

There are some really wonderful writers who, generally speaking,
are very introspective, almost intimate; great songs but not something I would feel comfortable performing; for example, Jill Sobule's 'Hodini's Box' or Aimee Mann's 'Jimmy Hoffa Jokes'.

If I had to make a choice, as a songwriter I would definitely prefer
to create songs that most folks could perform.