The F-100 was intended to be the supersonic successor to the F-86, and it was, just as the MiG-17 was to the MiG-15. That the F-100 wasn't powerful/agile enough to fight something like a MiG-17 doesn't change the fact that it was designed/purchased to be an air superiority fighter when speed was considered king.
The F-104 was Lockheed's answer to the complaints of pilots fighting the MiG-15 in Korea: speed, acceleration, climb, altitude to control engagement/disengagement. Its sole purpose was air superiority when originally designed and flown.
While the USAF eagerly accepted the F-4 after evaluating it, they did not ask for it. The F-104 was going to be the contemporary air superiority fighter. But the F-4 was generally as good or better than each of the different USAF aircraft it would ultimately replace. How could they not accept it? But it was really an interim air superiority fighter until the FX project could enter service. The FX started out being a large Mach 3 aircraft, possibly with a swing wing looking a lot like an F-14 Tomcat with similar weight. The Fighter Mafia was able to show that power to weight and wing loading were critical parameters for a successful fighter as well as a bubble canopy, so instead of building a Mach 3+ MiG-25 killer with limited maneuverability like the F-111, we got the Mach 2+ F-15 Eagle.
Summarizing the above and ignoring production numbers and service dates, the air superiority role was fulfilled in the USAF as follows: F-51D->F-80->F-86->F-100->F-104->F-4->F-15->F-22.
There are some big gaps in the F series numbers due to the numerous interceptors and strike fighters built in the early years and the crossover with the Navy numbering system in the 1960s.
In many ways, the F-16 is better than the F-15 for air superiority other than a smaller/weaker radar. But it is employed as a strike fighter with a secondary air superiority role. Whereas F-15C pilots are almost exclusively trained for the air superiority role. If you study the service dates, only the F-4 and F-15 are significant. The technology changes so fast that the F-100 had barely entered service before the F-104, MiG-21, and F-4 were starting to fly. But exponential cost increases trapped almost everyone at the F-4/F-15 tech level all the way to the present with F-4s and F-15s still serving in significant numbers and F-22 production cancelled at about 200. If you go by service dates, the F-4 is king. But the F-15 has been flying since the mid 70s and claims to have a perfect record as well as remaining a front line air superiority aircraft of the USAF due to the low numbers of F-22s. Unless Korea or the Middle East goes really hot, the F-22 will never have the combat record of the F-4 and F-15. Due to their cost, the F-22 will probably never serve as long either like the F-117 that is already long gone.