Luke and John said why they wrote; Matthew and Mark didn’t.
Some later wrote them to harmonize these four.
Jefferson wrote a gospel with a razor. Reynolds Price wrote one, too, using Mark as a tree and material from the other gospels and elsewhere and his own informed imagination as leaves. (Price is part harmonizer, part inventor, and part Jefferson.) Each term, Price even makes his students write gospels.
Why write anything? I think it’s push and pull, attraction and revulsion. And the need to add our own testimony, even if only as editors, commentators, or (like me) marginalists.
[I'm reading John's gospel. My reactions here vacillate between notes -- a list of impressions -- and something less sketchy. A note on nomenclature: the note number in my post's title indicates the chapter of John's material I'm reacting to. A title's letter, though, differentiates the post from earlier posts about that chapter. "John field note 2c," then, is my third post about something in John's second chapter. N.B.: 12a may precede 3d: I skip around.]