If they shipped with open source firmware, you would have a number of companies copying it and using in their products undercutting the original manufacturer.
The US and the West don't have teeth when it comes to IP violations in Asia.
If you can't do anything against IP violations, closed source doesn't exactly protect you from clones (the range of reverse engineering/firmware extraction services available is impressive). It'll slow them down, but also gets in the way of your legit customers.
That is true, but without source code the violators cannot improve "their" products much nor give any meaningful updates, so the original manufacturer can still have an edge.
If sources were available, the violators could even make it better than original, without having to make even remotely the same R&D investment than original manufacturer.
Not sure this applies much for the ROM's on microcontroller. They're pretty small and mostly handle very low level details so there doesn't seem much space for meaningful improvement. Even when the firmware is completely open, the original firm often maintains a competitive edge because they have the know how to work with the code base and rest of the chip. Ideally they have internal simulation tools, a broad range of expertise, etc. The firmware often doesn't contain as much "secret sauce", but does contains lots of possible vulnerabilities or bugs for customers.
