The whole point of oxygen is that at high altitude there is very little of it, the extra oxygen input is needed to burn
fuel. At 30,000 feet the oxygen content is approximately three times less than sea level. That means over three times less engine power, this can be temporarily replaced for a few minuites by injecting oxygen. The RAF also trialled it, but it was less popular than Nitrous Oxide because LOX is incredibly dangerous for the ground crew (if you even spill a few drops on clothing which has any oil residue you will be set on fire, and if you spill on your hands you get very badly 'cold-burned'), and it requires very prescise metering to avoid engine damage as obviously any errors in injecting pure oxygen have a huge impact on air/fuel ratio so if you get it a bit wrong, its melted pistons time. Nitrous is a little bit easier to handle, and less sensitive to incorrect metering, so it became the preferred option for boosting high altitude performance for brief periods.