Thanks for the Dylan statement. That's nice.
To answer a couple of aspects of Kalo's question, disingenuous thought it may be:
Songwriting
Collectively, The Grateful Dead really were some of the great American songwriters. The songs of Garcia/Hunter and Weir/Barlow (or Weir/Hunter, or whatever), are significant contributions to the Great American Songbook. Random evidence:
Bertha
Box of Rain
Brown-Eyed Women
Candyman
Casey Jones
Cassidy
China Cat Sunflower
China Doll
Dire Wolf
Eyes of the World
Fire on the Mountain
Franklin's Tower
Friend of the Devil
He's Gone
High Time
It Must Have Been the Roses
Jack Straw
Mississippi Half-Step Uptown Toodeloo
Looks Like Rain
Scarlet Begonias
Ship of Fools
St. Stephen
Sugaree
Sugar Magnolia
Tennessee Jed
Terrapin Station
Truckin'
Uncle John's Band
Improvisation
They were great songwriters, but what they did with those songs - letting them become their own things on any given night, night after night - was very, very special. Their dedication to playing in the moment testified, on the one hand, to a faith in the songs as entities unto themselves that could stand up in constantly morphing musical circumstances. On the other hand - and this is just as important - it testified to their unwillingness to let the songs "settle" into concrete forms. They saw it all as a shifting form, and that's much of their greatness.
Oh, and some serious instrumental chops, too.