The F-2, F-3, F-4, F-5, F-6, F-8, F-9, F-11, F-80, F-82, F-84(both Thunderjet and Thunderstreak), F-86, F-100, F-101, F-102, F-104, F-105, F-106. Every single one of those was developed and introduced between 1945 and 1960.
I understand that technology was advancing quickly as designers began working with jets, but even so there are so many planes in that list that it becomes ridiculous. Even taking into account generations and different missions there are so damn many planes developed in 15 years. Considering the enemy in mind was the Soviets, whose primary strength was numerical superiority, wouldn't it have made more sense to pick a smaller list of aircraft and produce them out the ass, even if just to simplify the logistics train?
In general, the "why did the US military develop so many X during the Cold War?" question can usually be answered by considering a few factors:
Rapid technological change — WWII ushered in a bunch of new possibilities and the US was eager to exploit them all as rapidly as possible through the judicious application of money
Inter-service rivalry — During this period, the Army, Air Force, and Navy were each strongly trying to become the most dominant services, and often refused to cooperate on hardware. So you end up with massive redundancy.
The Military-Industrial Complex — We often use this term as a catch-all term for all things nefarious, but what it really refers to is the strong relationship that developed between military "consumers," industrial "producers," and Congressional "funders." (We could also add think-tank "suggesters" and university "consultants" as well to this powerful ecosystem.) During the 1950s in particular, and especially post-Sputnik, the incentives for all three of these groups to increasingly spend and buy became incredibly out of whack with regards to any forces that would try to restrain spending. This is why Eisenhower coined the term in 1961 — he was frustrated by it because even he, a military President, could not restrain the endless expenditure. (One nice example of this is that prior to Sputnik, the US was investigate six long to medium range missile systems with the intent on deploying only the best two of them. After Sputnik Eisenhower felt so pressured by public opinion and Congress that he ordered all six to be deployed, even though all of them were expensive and a couple of them were terrible from every perspective — including military usability and safety.)
The ethos of the "bleeding edge" — The US approach to making jets, missiles, boats, etc. is to value the most high-tech, high-performance above all else. It is so ingrained into our approach that I suspect most Americans don't realize there are other ways to value military hardware. (The Soviets, by comparison, were more concerned about keeping costs manageable, about integrating new hardware into their existing infrastructure, and having everything be easily repairable. They also valued mass-production pretty highly at all — they may not have the best but they would have the most!) It is definitely visible in jet fighter development specifically, where we threw a lot of money at trying to get what were often quite small "edges" over pre-existing models. This isn't to say the US approach didn't have its benefits; sometimes with military hardware, the bleeding edge does give you a disproportionate advantage, and when you are contemplating how you are going to fight a war against an enemy with a troop force much larger than you can hope to match, maybe you do need to rely more on technology to make up the difference.
The lack of centralized control — One of the factors running through all of this, especially in the pre-1960s, was the fact that there really wasn't very much centralized planning behind the US approach to this. It wasn't like the heads of the military were sitting down with the civilian leadership and saying, "what is the optimal situation for our country?" There were a multitude of different avenues by which different requests were fielded and one of the results is that you end up spending a lot of money on things that end up coming and going pretty quickly. McNamara attempted to reign this under centralized Pentagon control in the 1960s but it's not clear how effective that was in the end.
You see very similar trends, incidentally, with the development of nuclear warheads and missiles, for all of the same sorts of reasons.
I have an article you may find useful if you are curious about further reading on this: Leon Trilling, "Styles of Military Technical Development: Soviet and U.S. Jet Fighters, 1945-1960." He puts a lot of emphasis on the different institutional contexts, and the main advantage to this kind of article is that it lets you see the "non-naturalness" of both the Soviet and US approaches to making jets. I can send you (or anyone else) a PDF of the article if you PM me. (It is in a somewhat obscure volume on the history of military technology from the late 1980s.)
Just for comparison, Soviet fighter jets, developed and introduced during same period (1945-1960):
Yak-15, Yak-17, Yak-23, Yak-25, Yak-27, Yak-28, La-15, Mig-9, Mig-15, Mig-17, Mig-19, Mig-21, Su-7, Su-9, Su-11, Tu-28.