Fun fact: in some monitors, the EDID flash is writable via the HDMI cable (because the manufacturer forgot to wire the write disable pin to disable this). I know this, because my employer at the time shipped one like that (facepalm).

That means that your laptop can corrupt the EDID.

Windows and MacOS actually ship with a database of 'corrected EDIDs', in which they look up the EDID of your monitor and use instead the one in the DB, because they know the original is broken. TBF, I think this information is provided by the manufacturer.

If you don't need DDC for anything else, the monitor-swapping issue could be fixed by wiring a 4kb I2C flash chip to the DDC pins of the hdmi cable (in place of the monitor, and writing it with a copy of the EDID, with the serial number incremented. A lot of work though. Maybe there is a place for someone to make an HDMI cable with a small embedded microcontroller, for fixing this and other DDC issues.