Depends entirely on the database as to if they work and why. Oracle, for instance, has a native NFS client built into the database. Modern versions of MS SQL support running on SMB3. Postgres is fine with NFS as well.

The biggest issue people have with NFS is when they roll their own. To get performance they allow asynchronous writes | but this means the write cache can potentially be lost during a power failure. Enterprise NAS systems like the NetApp referenced above have battery backed cache so writes are never acknowledged until they're in a secure medium.

I think that's a good rule of thumb but you can certainly do it if you know what you're doing (which includes having the right hardware).

I don't know how to solve problem of stateful container and data storage so I tried to use a NFS for this and failed.

Not to beat the NetApp horse to death, but they've solved that problem (they just do a poor job of advertising it):

https://github.com/NetApp/netappdvp