They only care if you can make it work on channels it shouldn't, they don't care whether the code that controls it is open or not.
But yes, an open processor could help with a lot of open networking problems, even though it seems more like an engineering matter than research per se.
My feeling is that the software to accomplish this is already largely there, but the hard part of getting a design to the fab and actually getting anyone to adopt it isn't.
I think there would also be a number of regulatory hurdles to cross, since this would end up being essentially an SDR, and the FCC (for example) already seems to fear wide public availability for those.