You can do this with screen/tmux too...no need to connect to some server where you can't audit their code.
If both machines aren't separated by NAT, you could. Except you'd need to either share you local password or an SSH key with another party, which is pretty inconvenient.
But most of the time you can't directly SSH into your laptop at home because it's behind NAT, so you need an SSH bastion, and we figured it's not expensive to host, why not put one out there for free.
And the code is all on github. Teleport (https://github.com/gravitational/teleport) is the server/proxy part.