Idk about all machines ever, but I remember being able to access ssh over a serial port.
Though in that specific case for me, it was more of a necessity rather than just a quirky way of using ssh (due to the “machine” just being a dev board with a UART ESP32).
To access the serial port remotely you need to add hardware to bridge it to the network. Or you go up to the machine and plug in another computer with a keyboard and monitor to access it directly.
There is/was a tool called x2x, which somehow let you send your input (mouse/keyboard) to another machine (I think via X forwarding tricks, although I don’t know how it worked, so I could be wrong).
I tried it around a decade ago and at the time it felt a bit abandoned. I vaguely remember that it might not have worked with every window manager? Anyway, I assume it hasn’t got better supported since then. But it did feel magical.
Later, things like x2vnc made the idea more cross-platform (X on the local unix-like box, VNC on some other platform), but only with two machines.
After that, Synergy became a thing, and supported many machines, but then they eventually went to a model that tended to require payment.
Later, Barrier forked from Synergy, and it allows much of the same functionality. It's still very free, and it still works, but it's kind of abandoned.
Today, there's Input Leap. It is (naturally) a fork of Barrier, and it is still sees regular development.
So, you'll accept any solution, except the existing ones that work?
XDMCP solves this exact issue. You use one device which becomes virtually an attached terminal of another device which is actually headless and with no input devices of its own. We've had this for 30+ years.
No, we already use the solutions that actually work, and are speculating why there isn't one with the simple, obvious user experience. Why shouldn't we?
…except for when they can’t. The relevant retort would be that I could instead be using hardware with a remote management interface like IPMI, and building a custom OS installation image with remote access preconfigured. But even then I’m not sure how you’d have me troubleshoot surprise network issues.