Is that really why? I know many devices where I can just set whatever country I want :)

This is handy sometimes because in the EU it's the opposite, the 5 and 6 GHz bands are much smaller.

So it's perfectly feasible to have an open source Wifi, or Bluetooth or any other RF, stack, but only certain compiled versions are actually certified. I understand that the openness in this case would be limited: you lose the freedom to modify and run the software as you wish (unless you want to risk to break the law), but you can still help bugfix, improve the software and verify that there no backdoors / spying features.

The reason sometimes given by vendors that "FCC demands the code to be proprietary" is an excuse.

The law does state that "an intentional or unintentional radiator must be constructed such that the adjustments of any control that is readily accessible by or intended to be accessible to the user will not cause operation of the device in violation of the regulations" (https://www.law.cornell.edu/cfr/text/47/15.15 )

So if the manufacturer makes a device where changing the firmware is "readily accessible" to the user and there is an open source firmware available that can circumvent the FCC transmission restrictions (for example, change the power limits or channel limits for wifi physical layer), then that could be grounds for FF refusing to certify that device, as it is not permitted to make, import or sell general unrestricted transmitters to the general public (there are certain exceptions for licensed operators, ham radio, experimental use by manufacturers etc).

It's similar to other clauses that prohibit manufacturers from making it easy for the user to modify the equipment - e.g. 15.203 (https://www.law.cornell.edu/cfr/text/47/15.203) "the use of a standard antenna jack or electrical connector is prohibited." so that the user can't easily replace the antenna with a different one from what was certified.