EEPROM...Which these days is pretty much the same as the generic "flash memory"
Nope. EEPROM is byte (or word) reprogrammable, flash requires one to reprogram much larger blocks of data.
"ROM" - to the end user, past and present - is software you can't change.
So, you're arguing that a device image which the user can change is also software they can't change. Whatever.
it's the same item
The same, except that one is physical, and the other just an image which could be downloaded. That you have a COCO II speaks volumes.