The concept on a surface level to have ownership over the data makes a lot of sense and to a large part the support exists in a fragmented manner across the different providers/applications.
The concrete idea of user having a database and then authorizing that to the service is highly impractical. It might be applied for experimentation purposes in highly controlled environment but cant scale beyond that.
1. Databases require maintenance, backups, failover
2. Schema update are nightmares. No one is ever comfortable with it, specially the bigger you are.
3. Authorization seems to be following one to many pattern here, one database and multiple applications. Its a no go in case of update operations