The issue in GP's idea is, that there isn't such a referrer field (his first sentence is correct). And even if RDP has it, the service would be limited to RDP, and GP's idea is probably to have it for any service thinkable, e.g. also SSH.

A solution on top of that would be for this obscuremyshit.com service to have a client-side listener. So if I get a hit on the page obscuremyshit.com/393nnasjhf83u98723401 from IP x.y.z, the obscuremyshit client running on the target cimputer gets a signal from the obscuremyshit server to "Open port 22 and allow a connection from the IP x.y.z" (I guess that means the client would have to be in control of the firewall rules), and then the computer with the IP x.y.z would have to establish a connection within a timeframe.

Of course it would get more complicated if e.g. the above URL is hit from a different IP address (e.g. from someone's phone over 5G, and the SSH connection wants to come from a laptop over a cafe WiFi).