"Most" supersonic aircraft are fighter jets and other military aircraft that use jet engines, not rockets. They may have afterburners that are much like a rocket that just injects jet fuel in the exhaust stream, but that's still using atmospheric oxygen.
The issue, I think, is more about balancing drag and air intake at appropriate atmospheric densities for different speeds. An SR-71 Blackbird could fly at 85,000 feet continuously, and a MiG-25 set what I believe is still the air-breathing record max altitude by pulling a "zoom climb" (accelerating in higher-density air that the engines could use effectively, then pulling the stick back and coasting up through rarefied air too thin for the engines) to 38km or 123,000 feet.
Most experimental hypersonic aircraft use rockets because that's what works.