http://www.time-travellers.org/shane/papers/NFS_considered_h...
The tl;dr basically boils down to the fact that PostgreSQL and MySQL (or really any good database engine running on *NIX systems) make very strong assumptions about the POSIX-ness of their underlying filesystem: flock() is fast, sync() calls actually mean data has hit disk, etc.
Docker/CoreOS/etc. aren't a replacement for a good SAN or other reliable storage. If you value your data I'd suggest keeping your core database(s) on dedicated machines/VMs (ideally SSD-equipped and UPS-backed). If managing those is too much work, consider a managed cloud database; DynamoDB and RDS can stand in for Redis and Postgres, respectively.