I can also remove my lights and breaks from my car and it will still work, but if authorities find out I might be in trouble.
Wifi is shared spectrum and devices using are licenced to make sure they conform to the local regulations. One size does not fit all. For example 2.4GHz wifi channel 13 is legal in EU, but in USA it falls on a govt owned band. This is why companies like Mikrotik or Ubiquiti have specific hardware versions for USA. So that they verifiably cannot be set on illegal channels by the enduser.
The reason sometimes given by vendors that "FCC demands the code to be proprietary" is an excuse.
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.
This is handy sometimes because in the EU it's the opposite, the 5 and 6 GHz bands are much smaller.
The reason the modules with integrated antenna are so popular is that the module carries its own certification, so you don't need to do it yourself.
If you use the module with an antenna connector instead of integrated, you must get your own FCC certification. It's for the entire system.
> Why can't one have an open source stack with specific builds that are approved, tested and certified?
Mainly because it's heinously expensive and difficult.