Back when I had two monitors, I got the same cables for both and I indiscriminately plugged them into my computer (I had a laptop, so plugging/unplugging happened ~daily). So the mapping between computer port and monitor definitely wasn't going to stay the same.
Yeah, it would be a workaround for some cases but not all. It would work in the case of a desktop system where the monitors are always plugged in, and it would work for the case where the monitors go through some kind of USB-C dock (assuming it's possible), but not in your case.