Seconded. This is the standard CouchDB approach: one database per user.
Sounds weird coming from my Postgres and MySQL background, but works great in practice, depending on your use case and if you clear out old revisions and unused docs, which for our use case can number into the thousands fairly rapidly.
Everything in software is a trade-off. This trades space efficiency for multi master replication with first class offline app experiences.
For many cases, that's a fine trade. Disks are cheap. If that isn't a fine trade for a particularly large dataset, use a different technology that's better at space efficiency and worse at other stuff.
I let the user decide to logout and destroy or just logout if it's a trusted device but obviously the local db could be accessed. Most users don't logout and I set a long cookie expiration.