> By the same reasoning, one could build a piston engined supersonic aircraft...
Now that's a thought provoking engineering problem! Assume a supersonic propeller is required. Using the Thunderscreech as a baseline, which admittedly didn't quit go supersonic, but it gets us close. Its powerplant produced nearly 6,000 horsepower. That is certainly doable with a piston engine, top fuel dragster engines produce roughly 10,000 horsepower. For about ten seconds.
If this plane burned nitromethane, it wouldn't even need much atmospheric oxygen, nitromethane required roughly one tenth the amount of oxygen per mass of jet fuel. Of course, this means it has to carry a lot more fuel
https://en.wikipedia.org/wiki/Republic_XF-84H_Thunderscreech...