Once called up a busy class B (4th busiest in world at the time, LHR around 15th) and requested an overhead transit. Approach told me my mode C was indicating FL410, I said sorry and will get it fixed and should I turn it off, approach said keep mode C on and immediately approved my transit request. No doubt I was causing TCAS mayham up in the flight levels but ATC didn't care, and neither did I
One can transit overhead LAX in the SFRA with Mode C and without a clearance (but monitoring a certain frequency). Off the top of my head there is the Hudson river corridor, and Class E corridors at SAN that cross short final. There should be no reason why a similar approach to controlled airspace cannot be made in these somewhat smaller airfields too. The powers that be just have to make the effort, so I guess it will never happen.