For the sake of discussion, I'd like to throw out the following. The US Congress contracted for the Allison V-1710 and development started in 1929. They anticipated a high-altitude requirement and developed a turbo-supercharger system for the Allison V-1710. It wasn't perfect but was exactly what was contracted for. After the prototype P-39 had some issue, they deleted the turbo-supercharger from the aircraft and all subsequent fighters except the P-38.
As a result, all the subsequent fighters except the P-38, while pretty good at low to medium altitude, suffered from lack of high-altitude performance.
Unfortunately, the US Congress owned the design, lock, stock, and barrel. I submit that they should have taken the simple step of appointing an Allison manager for the government and delegating him the authority to oversee improvements to the engine.
Next, he could have asked Allison to pursue a development of the 2-stage, 2-speed supercharger to augment the turbo-superchargers, which were earmarked for the strategic bombers, so they could reach high altitude. We had insufficient quantities of certain metals to allow the number of turbochargers for there to enough for the fighters, according to the war materiel board …but we didn't need those metals for superchargers.
We still would have needed the time to sort out the issues we found in Europe with the early P-38 deployment. Those issues were the intake manifolds and running on European fuels, with had a much larger percentage of aromatics than did American fuel. Once these were sorted out, the engine problems "went away" and the P-38 had no more difficulties at high altitudes. Most were transferred to the Pacific where they gave yeoman service and were the mount of our two top-scoring Aces, Bong and McGuire.
Meanwhile, if the Allison V-1710 had seen a concerted development effort to field a 2-stage, 2-speed supercharger installation, I feel pretty certain they could have closed in on a good development effort and done it in a reasonable time. In point of fact, the late model Allisons with the auxiliary stage supercharger flew at high altitude very well and made as much power as any high-altitude Merlin. But the auxiliary stage was a dead end in my mind and I am proposing they concentrated instead on an integral unit, such as the Merlin had. Maybe even if we had not built Merlins, we could have consulted with Sit Stanley Hooker on the supercharger design.
I do NOT claim we could have done it exactly quickly, but it could have been done and would have resulted in good things for the V-1710 in time to make a difference in the war.