Lots of designers realize that memories are a potential source of trouble, so include diagnostics in the firmware. Given that there's no realistic way for a technician to find a memory problem, a little software designed to pick up these will sure make you friends in the test department. If your boot ROM is totally misprogrammed or otherwise non-functional, then there's no way a ROM test will do anything other than crash. ROM test working. The odds are against it, and somehow Mother Nature tends to be very perverse.
Some developers feel that a ROM checksum makes sense to insure the correct device is inserted.
This works best only if the checksum is stored outside of the ROM under test. If this one device functions, and you write the code so that it runs without relying on any other ROM, then the test will pick up many errors. It's pretty easy for a couple of errors to cancel each other out. CRCs are notoriously misunderstood but are really quite easy to implement. On a Z80 0xff is a call to location 38.