Shortround6
Major General
Even just a two speed Allison would have been a nice asset to have - just look at how much better P-40F performance was over P-40E.
The supercharger itself may have been too small.
The -33 engine in the long nosed P-40s was good for around 1040 hp at several thousand feet below where the Merlin III made 1030hp and the supercharger only had minor changes aside from the supercharger gears. The Merlin XII in the Spitfire II moved that up by about 2,000ft and the Merlin 45 with the Hooker designed/modified inlet Mover that up another few thousand ft.
What the Merlin XX did for the P-40F was to use an even higher gear than the Merlin 45 used (but not by much) and couple it with low gear that allowed a good amount of power for take-off or low altitude flying.
Just putting two gears on a standard Allison supercharger doesn't get you much better performance than the 9.60 gear engines at altitude but it does allow for higher take-off or military powers at low altitude. Merlin XX had around 100hp for take-off over a Merlin 45 at the same boost and RPM because it's low gear didn't take as much power to drive and it heated the intake air less.
100/130 fuel and WEP settings reduced the need for low gears in the superchargers.