Now, there's an old saying that "if it looks right, it'll fly right", and to my eyes the P-40 always looked right. Not just the shark mouth, but the sleek lines and the pointy prop spinner, although I admit the undercarriage could have done with some work. Nonetheless it looked like a modern, high-performance monoplane fighter, but all the way throughout the war its performance lagged behind its contemporaries, less so as time went on but still enough to tarnish its historical reputation. I understand that earlier versions had a limited supercharger that neutralised its high-altitude performance, but even when fitted with Merlin engines and lightened the aircraft always seemed to be a few dozen MPH slower than the competion, a thousand feet per minute less sprightly. Having said that, it's impressive that a design dating back to the days of the Hawker Hurricane was still getting kills in 1945,* and it seems to have defenders, not least because it has always been kicked around like Richard Nixon.
So, was the P-40 doomed by a fundamental, insurmountable design problem - perhaps an aerodynamic deficiency - or was it just limited by a combination of things that individually might have been debugged, but collectively held it back? Was there enough horsepower in Christendom to make it a worldbeater, or could it have been tidied up aerodynamically, a la the Bf-109F? I surmise that the scoop didn't help, but other, faster aircraft also had large chin-mounted scoops (the Typhoon springs to mind, although the Tiffie had considerably more horsepower). The P-40Q turned it into something almost but not quite as good as a contemporary P-51, by essentially replacing everything except the cockpit seat, but by that time the P-51 existed, and so the P-40Q was abandoned.
This intrigues me because, in most other cases, I can see why other early war fighters couldn't keep pace with technological developments. The Zero relied too much on light weight and a big wing for its performance, and when the aircraft was fitted with armour and self-sealing tanks it was no longer lightweight, and the big wing held back its top speed; the Hurricane's frame construction meant that it was just too heavy, with a thick wing; the 109 was too small to contain the equipment it needed to perform a relevant role as the war progressed without modifying the structure to such an extent that it was no longer sleek, which necessitated a larger, heavier, more powerful, torquier engine that taxed the landing gear and the wings, thus creating a kind of negative feedback loop, etc. In contrast the P-40 was at least capable of great speed in 1940, in a dive, and the basic design looked good.
Reading up on its history I get the impression that the earlier YP-37 - a long-nosed P-36 mod based on a turbo-supercharged Allison V-1710 - would have been a wiser long-term choice, but I'm sure they had their reasons for cancelling it, not just the awful cockpit view.
* Which seems to be about a year longer than the Hurricane itself (the last confirmed Hurricane kills I have read about were in 1944).