> why would that need a blockchain (even without proof of work), as opposed to simple signed, timestamped, indexed posts and having the reading client app check the signature and post indices?

Yeah, that's exactly what SSB does, plus each post includes a hash of the previous post.

I think that's so that even the holder of the private key can't retroactively replace an old post with an altered version of that post (but with the same index number and similar timestamp).