The issue with Dat, Mastodon, SSB, Diaspora, etc. is that they do not solve the problem of who's running the servers. They give you the tools to easily sync and migrate data that can back a social network, but you still need a live machine to host the files. These systems don't specify how to find those machines and how to compensate the people running them. The result is a cobbled-together list of servers posted on project web sites as a "temporary" way for people to get started.

Cryptocurrency could potentially provide an avenue to compensate anonymous storage providers for storing encrypted data backing a social network. A well-integrated system could give users the one click to join experience you need to get wide adoption, without forcing them to think about who runs their server.

This is what Blockstack and many other projects are trying to do (I don't know about Blockstack in particular, it didn't work when I tried it a couple months ago and the founders seem to grandstand a lot).

Not sure if this is exactly what you are looking for but I just stumbled upon the Dat project myself.

https://datproject.org/

Thanks! A system after my own heart, it even uses a Merkle tree instead of a blockchain <3

Does this have a system that allows users to keep ownership of their personal data?

Yes, the data is owned by you and signed for ownership attribution. AFAIK there is no "remove my data from the network", as it is a public network.

You should also check out Beaker Browser. It is a browser built around the dat protocol. Really great community and even has a few decentralized social networks already.

https://beakerbrowser.com/

I almost forgot crypto projects could exist without an ICO. Shit's crazy.