F-8fanatic
Consider it like this--I like to look at the "what-if" theory. What if there was no P-47 or P-51? The Warhawk could never have performed their roles nearly as well. But, if the 47's and 51s had to perform the Warhawk's roles, could they have done as well? They would have actually done better. There's your answer.
From a sheet of paper and prototypes? 
The first P-47 combat mission occured in March 1943, the P-51B entered production in 1943, and didn't began escort missions until January 1944.
With those time spans you need to be looking at:
P-40Q which did have a supercharger for high altitude flight at 422 mph, and could have been in production by 1944.
P-60C (P-40 with an R-2800 radial engine) which had a supercharger and could do 405 mph at high altitude. It could have been in production in 1943/44
P-63 (improved P-39) which had a supercharger and could do 410 mph at 25,000 feet.
These became foot notes because by that time the P-47 was in service and offered even better performance with a top speed of 433 mph, and the P-51 was entering service with a top speed of 433 mph and exceptional range. The older aircraft were finally breaking 400 mph, as the new breed approached 500.
The P-36 / P-40 design was 6 years old, and had been in service for 2 years when the P-51 was first dreamed up by North American.
The P-47 was more evolutionary originating with the P-35, then P-43 and finally P-47, but it was a major improvement (the reason for the new designation). It's earlier relatives were notably inferior to the P-40 and not used in quantity (about 300 total).
So sure, the P-47, P-51 could have done the job better, but that is kind of like comparing the P-51 to the F-84 as a WW2 air superiority fighter, better but it simply didn't exist in that time frame.
The Spitfire and Me-109 came from the same time period but saw continual development, while the P-40 peaked in 1943 when the USAAF wisely adopted newer designs with more long term growth potential, that would not cause an interuption of P-40 production. Somehow for many "something even better" has translated to the P-40 was a turd.