What I use Tumblr for is basically to read supplementary world-building blogs for stories/writers I already like, look at pretty/fun art, read random interesting stuff people post links to, and sometimes get updates on fics I'm following faster than AO3 can process and email me about said updates.
Also I like Tumblr's "like" button because I am a massively lazy person and appreciate a way to say "hey, this is neat, thanks for posting it" without having to actually type those words over and over. Plus you can do the equivalent of giving kudos for each chapter update on WIPs, whereas AO3 will not let you give kudos more than once to any single fic regardless of how many chapters it has, so it's also a useful way to signal to a writer that people are, in fact, still reading a multi-chapter story... again without requiring me to actually type up a comment when I have nothing to say beyond "hey, still reading this."
no subject
Also I like Tumblr's "like" button because I am a massively lazy person and appreciate a way to say "hey, this is neat, thanks for posting it" without having to actually type those words over and over. Plus you can do the equivalent of giving kudos for each chapter update on WIPs, whereas AO3 will not let you give kudos more than once to any single fic regardless of how many chapters it has, so it's also a useful way to signal to a writer that people are, in fact, still reading a multi-chapter story... again without requiring me to actually type up a comment when I have nothing to say beyond "hey, still reading this."