I think people are forgetting about one important factor...cost. (Both dollars and resources to build). Morningstars might be really awesome fighters, but if a Hellcat is 80% as good at dogfighting, a Thunderbolt is 80% as good versus capships, and both are 25% the cost, then a lot of carriers are going to carry Hellcats and "Thuds" instead of Morningstars.
(Actually, to my eye, the Hellcat and the Morningstar have a very similar looking design. I had wondered for the longest time if the 'Cat might be a production scale fighter built using technology pioneered for the Morningstar, but LOAF shot that idea down for me by pointing out that the 'Cat probably pre-dates the Morningstar. It's still possible they leverage similar technologies, but the superficial similarities might just be because those design features were the best ways of doing things...kind of like why all fighters designed from the mid-70's up till the ATF's came out all kind of looked the same, regardless of nationality--similar wingforms, twin engined, twin tail (the FA-18, the F-15, the Mig-29, the Su-27, etc.). It just makes engineering sense. But I digress).
The comment about the European theater versus the Pacific theater is interesting. Actually, the Allies DID use P-51's and P-47's, and especially P-38's in the Pacific, as well as in Europe. However, the reason why you see Wildcats, Hellcats, Avengers, etc. more often is a difference in operational requirements. In the Pacific, fighters were either operating off carriers or hastilily constructed, often rough, island runways really close to the action, or from established bases very far from anything. So they either needed extremely long range (like the P-38), or the ability to take off from a short, rugged, often pitching runway but not needing a whole lot of range at all (all the Carrier planes). Performance was meaningless unless you could meet these requirements, so even though a P-51 could outperform (in most respects) a P-38 or a Hellcat, it wouldnt' have been usable in either of those two roles.
On the other hand, over Europe performance was more of a premium, and operating conditions were less stringent, and so you saw different fighters prosper there.
The cost issue is highlighted as well. In China and the USSR you saw a lot of P-40 Warhawks and P-39 Aircobras, because these fighters, although underperforming, we cheap and all the Chinese and Russians could afford (or at least, that we were willing to sell them on the cheap).