You don't need all the firmware to be read-only, only the firmware update code, which can then require a hardware jumper to be set in order to update the firmware. Then the firmware can't be corrupted without physical access to set the jumper, and even if it is, the owner can still re-flash clean firmware because the update code is strictly read-only and therefore still clean.

And you already need to be able to at least detect that someone has had physical access, otherwise you can't even be sure that the device hasn't been replaced with a compromised one that forwards your credentials to the attacker.