TLDR: Use a complicated SSH proxy instead of a VPN.
This has some serious downsides for non-SSH applications. For example, to connect to a production database cluster, one would need to ssh through the proxy to a bastion host, and then set up port forwarding from the bastion host to the database. Setting up a simple database connection now requires shell access to a production server. This is less secure and more complex than using a traditional VPN.