> Teleport Proxy itself doesn't have access to much, so exposing it to the Internet is fine.
yeah this is a bad idea in general. If you have critical stuff you need to SSH into from the public internet, keep it all in private IP space and have an openvpn gateway (or IPSEC VPN) with a public interface, and a private interface facing inwards towards the hosts.
you should not even be able to route to the IP of the thing you want to SSH to unless you've authenticated to the VPN and your client device has been handed out an IP in your RFC1918 IP space.
a machine like an openvpn gateway can also serve the purpose of getting you access into an OOB network (example: a public facing IP on a 100Mbps DIA circuit you've bought from a totally diverse ISP in the same colo, with a static /30), which has access into internal IP space devices such as serial console servers and ssh bastion hosts.
authenticate the clients by a unique public/private key pair per client device. Easy to revoke a specific device's key from the server side if needed.