The actual best open source Dropbox replacement already exists: SeaFile. Too bad their website is terrible.

https://www.seafile.com/en/home/

It's pretty magical. It nails the "online" vs "cloud only" paradigm via the SeaDrive client. I have it running on my file server, and now all my machines have access to terabytes of storage with local performance, since it can cache a subset of your content locally.

And since I can run the server on my LAN, the throughput is way better than Dropbox would be too.