In my humble opinion, the reason the P-40 would never be a great fighter was because it was draggy. Giant bulbous fairings over the open-wheeled gear wells, bulky, sturdy, but thick and draggy wings, giant front intake (from E onwards) and a high abrupt cockpit.
The fact that P-40 pilots didn't notice hardly any difference between Allison-powered and Merlin-powered P-40s tells you the power supply wasn't the problem. It was the underlying design. It worked. It simply stopped working any better after a point.
I love the shape of the P-40s, though. One of those classic, nay, iconic, airplanes that lends to childrens' imaginations!
You don't get that with F-22s' looks, or F-35s. So folks look to the past designs to daydream about (myself included).
The "giant intake" is actullay the oil cooler and it has a very large exhaust opening at the point where it blends back into the body (I know, kinda hard to see sometimes).
As fibus mentioned, the P-40 is actually the
streamlined version of the H75 airframe and thus, the modification allowed for the frame to have its own designation - H81 (later improved with the H87).
The Allison was used because it gave more power in a more streamlined package, compared to the H75, or "P-36" as we know it, and from whence the P-40 originated.
I believe the calculation commonly cited is "more power per square inch of frontal area".
However, what you are citing is the "deficiency" of an older design.
At the outbreak of WWII, we only really had 3 fighter planes that could even hope to be a match for the fighters in the Axis arsenal - the Wildcat, the Buffalo and the Warhawk.
All 3 designs are based more on experiences gained during WWI, with some updated engineering to further streamline the airplanes.
Later experience would show that we needed to move in a different direction with our designs, and that yielded some planes that are remembered as some of the best of the war - the P-51 and the F6F, just to name a couple.
However, without that data to fall back on, the planes we used early in the war was as good as it got for us.
Its just an older design, but even so, the P-40 is actually a very good example of a later pre-war design.
The reason Performance didn't change much with the change to the Merlin was because that Merlin was setup similarly to the Allison, i.e., single stage/single speed supercharger.
This limited the capability of the Merlin, almost to the point to where it was indistinguishable from the Allison, from the pilot's perspective.
Had Allison and the USAAF worked closer with the British and tried harder to adapt their two-speed/two-stage supercharger to the V-1710, the P-40 would have probably performed much better.
As a matter of fact, Allison did realize the benefits of the improved supercharging system and did try to develop one for their engine, but it was an inferior design, basing itself off the existing supercharger, so performance never achieved the levels it did with the Merlin.
Our own "Clay Allison" has struck upon a novel idea, which is to replace the Allison, not wth the Merlin, but with the even more powerful Griffon engine.
Even if an early version were used (which would be similar to how the Allison was set up), it would still put out superior HP numbers and may have given the plane the capability it should have exhibited.
Elvis