The biggest problem is that most mining hardware are incapable of directly establishing the VPN connections themselves. This complicates the client-side setup. The pool user would need to set up some kind of host in their local network to run the VPN client and also some kind of stratum proxy that accepts local connections and forwards them through the VPN.
If you cared enough about privacy, it would be more flexible to set up an SSH server on AWS and forward your stratum connections through an SSH tunnel to any pool of your choice. You can change the AWS instance periodically and get a new IP address if you are that paranoid.