That makes it tough to inspect the fixed cup as well as you can when you remove it, IMO.

I always remove it, clamping blocks of wood on either side of the BB to hold the fixed cup wrench on the fixed cup and then hitting the end of the fixed cup wrench has never failed me, and generally they spin right out without all that much of a fight anyway. Cleaning up the threads with a wire brush followed by some fresh grease makes me happy!