Picasso (supposedly) drew on a napkin, and Banksy draws on derelict walls or sticks his work through a shredder. The medium doesn’t need to be lasting.
Edit: The potentially short-lived medium was chosen by the above artists. Tumblr users many not be too happy if work is lost.
banksy's walls are sold though; and he is still kind of the exception because of his art format. Not everything needs to be lasting but 100% temporary art is not common.
Oh, it's more common than you think, only it being highly valued is rare. That doodle you drew while having a conversation on the phone? That's throwaway art, even if you don't consider yourself an artist.
How many do you think they would be willing to pay some small monthly fee? I'm guessing most of them think their work is worth at least $5/month, right? Maybe Tumblr should become a paid service and ditch the advertising model. That way they could be more relaxed about what types of content they are willing to host.