Crucially, in order for this concept to work, the two sides are supposed to be totally independent -- the computers are different, the displays are different, and the sensors are different. However, at any one time, only one FCC is active, in that it is actually controlling the plane. Comparing the two sides AoA now violates this assumption and so many of the other engineering and certification assumptions may be violated since now the two FCCs are sharing AoA inputs.
Furthermore, my understanding is that now that everything is being looked at more closely, the FAA is having a change of heart about the idea of having one FCC active at a time being acceptable. If there is a hardware fault in the FCC, it has a lot of authority to cause problems, possibly faster than the crew can resolve them. My understanding is that now the FAA wants the FCCs to cross-check each other. Making this happen will require a lot of engineering and testing, and I think that this is the big reason for the delay. The MCAS fix itself was flight tested way back in April and May of last year.
All of that said, I don't believe an FCC fault has ever been implicated in an accident, so this IMO doesn't really present a safety issue big enough to be relevant to say, my decision of whether to fly on a 737MAX, but it looks like the FAA is deeming it not adequate for certification.
Airbus of course uses a different philosophy and uses multiple FCCs that continuously compare their output and vote.