Just a note: The P-38, P-47, And P-51 were NOT designed from the outset to be long range bomber escorts.
The P-38 was originally intended to be a bomber interceptor. Good speed, climb, armament, high altitude performance, and a fuel duration of 1 hour at full power were design criteria. It wasn't meant to slug it out with single engine fighters.
The P-47 was designed as a high altitude fighter, hence the turbo. Extreme range wasn't a major design goal until the N was developed.
The Mustang was designed in response to a British request for North American to build P-40s for them. NAA thought (quite rightly) that they could build a better fighter than the P-40, and proceeded to do so in very short order. However, the Mustang I (like the P-40) was powered by a non-turbocharged Allison V-12 and therefore its high altitude performance was less than stellar.
In their initial incarnations, none of these three had the combination of range and high altitude performance needed for the escort role. This was partially due to a pre-war Air Corps doctrine that forbade the use of external stores on pursuit craft.
The reasoning for this was to avoid the added drag of external fuel tanks and to prevent ground commanders from using their pursuit ships for ground attack. BTW, this policy essentially dictated that Kelly Johnson and Lockheed use a thicker wing on the P-38 than they would have liked in order to provide internal tankage for the required fuel load. It wasn't until Jan. 1942 that the ban on external stores was lifted.
Another contributing factor was the American belief that large formations of heavy bombers would be able to adequately defend themselves on their way to and from the target. It wasn't until the Luftwaffe began destroying the bombers in appalling numbers that the Air Corps realized that A) the bombers did in fact need escort, and B) they had no purpose built type to fill that role. Only then were existing types adapted to fill that void in the inventory.