I don't think results have proven the F-15 was needed at all. It's only combat prior to the US entering the Gulf was in Israeli hands where its glaring fault, that its design technology was ahead of the weapons technology to support it was prevalent. The Israelis wound up using them just like the US used the F-4 in Vietnam because of the shocking poor performance of 70's gen sparrows and sidewinders (the reason the Israelis developed the Shafir which is a generation ahead of the Sidewinder like the Archer or that South African missile). Actual combat reports in encounters with MiGs involved firing off all your missiles at once trying to hit one target and frequently missing, then getting a gun kill on a Fishbed through sustained manoeuvres, in these cases the performance of an F-4E would be just about the same, the main factors here being excess thrust and boosted controls.
The Sidewinder of the period had only just overcome the tactic of using g-manoeuvres to break its lock, but it still liked clouds and random heat sources. Sparrows were still just about useless, scoring maybe 1 in 3 shots fired and half the time just plain going ballistic after launch.
The Israelis did like the Eagle because of its terrific all round performance, they were used to dogfighters like the Mirage and it still had the weapons and intercept qualities of a Phantom with a newer tech avionics fit and especially its powerful radar. But those crappy era weapons ca.1978 still meant basically you saw the enemy well far away but still had to close to the same type of combat you'd be in using a Phantom or a Mirage anyway, because the weapons tech couldn't keep up with the plane tech. The Israelis jokingly referred to it as "the flying SAM site" because you had this powerful radar, waited for the enemy to finally close to combat range, then fired a whole lot of missiles, nevertheless the name isn't all that affectionate since the Israelis respect gun kills and dogfighting over any other aerial combat (mostly because guns don't fail on you). Upon closing to combat range Israeli pilots say they routinely ignore everything going on inside the cockpit with the avionics anyway, which is understandable considering the poor reliability of pre-80's-digital era.
The Eagle was like a glimpse into the future, a very, very, very expensive one. One should recall it was a knee jerk reaction to unreasonable paranoia about the Foxbat. You could've put the Eagle in production five years later and saved a bundle, but my point is it was still not strictly needed at all. It didn't actually serve any physical purpose which couldn't have been handled just fine without it, at a savings of several thousand million dollars, quite simply the United States would've been a wealthier country without it, you might've had free universal healthcare in 1976.
The F-16A was placed in service in 1980 and if I'm reading my Janes right in 1981 (block 5) it had Sparrow capability and a couple of other improvements (databuses and the like). The AN/APG-66 was pretty good with digital multimode, pulse-doppler and angle track, it was well ahead of anything in the Soviet arsenal before the Foxhound.
There's a couple of things to consider with the "fantastic Eagle performance" in that some of it, a good part of it is illusory because we're incorrectly comparing a 4th warplane with 3rd gen warplanes on that score.
As mentioned firstly weapons tech wasn't really up to 4th gen standard in the 70's, 4th gen is an 80's thing. It's like having a great new assault rifle with only black powder and ball to load it with.
Its engineering requirements, whilst achieved under test conditions are only partly achieved in service trim. First point is the 1.8 Mach speed restriction under normal combat conditions. There's an engine management system override switch inside the cockpit which was used to achieve its design requirements of a 2.5 Mach top speed (clean and specially prepared), but if used once the engines require a full tear down maintenance immediately upon landing.
Its other requirements were based on Vietnam experience in Phantoms, where it was found they manoeuvred well compared to MiGs at low altitude because of excess thrust and twin engine reliability, so improving on this theme of dogfight capability was listed. Borrowing industrial technologies from the blown out Valkyrie project were used for this. And of course a gun was mandatory.
The other requirement was extended ferry range for European deployment, achieved by aerial refuelling, external tankage and stripping (combat fit is carried in an escorting KC tanker's cargo hold). Unrefuelled range in combat trim isn't all that spectacular.
So it has great 4th gen (ie. honeycomb, body lift, good avionics fit) performance both in dogfight at low alt and BVR or intercept performance. But we're still comparing it to 3rd gen warplanes which is all wrong.
The thing to keep in mind is in the common 4th gen combat environment the Eagle can't dogfight on equal terms with an F-16, Hornet or a Fulcrum at low altitude. No way. I mean you can still win and it comes down to pilot skill, but just on the face of it these lightweight, dogfight specialised 4th gens have the standing advantages of sheer thrust/weight, specific thrust/altitude ("spooling" if you like), nimbleness, very high g-capability (the F-16 and MiG-29 were both specifically designed for 12+g without breaking although a pilot isn't supposed to exceed 9g if he wants to stay conscious and external stores can restrict it further depending what is carried).
So take the Eagle into an environment of technological parity, which is to say the period where its vision is kept up with by industrial tech commonality, and it's just like the Phantom was for a 3rd gen fighter, a heavy weapons platform designed for medium altitude BVR and sustained air superiority rather than agile low alt dogfights against lightweight 4th gen contemporaries like the F-16 and Fulcrum. But even so it can do dogfights pretty damn well. This was the same story for the Phantom up against Fishbeds, can do it but if you had the chance a medium alt missile kill was a safer bet if the missiles actually tracked for a change, and sustained transonic manoeuvres were the preferred mode of close combat (avoiding the benefits of a lightweight fighter).
The Eagle was a step ahead only because it was rushing something everybody was headed towards, at terrific cost, for an advantage that was both unnecessary and short lived.
In 1975 a force of Phantoms and F-5's are going to be perfectly contemporary against any Soviet threat. The Eagle had no advantages over the Foxbat from the Phantom (another conversation but my sources are Israeli combat records of Eagles versus Foxbats, mostly they all fired off all their missiles at each other without hits and then the Foxbats disengaged at a whim and were uncatchable, and Israelis have been known to chase enemy MiGs all the way to Egypt and get turned back by AAA over their home bases, if they could any way have caught a Foxbat in an Eagle, they would've).
Then in 1981 a force of Block 5 F-16A's and F/A-18 Hornets are already replacing the Phantoms, which is timely and still gets 4th gen fighters on the front line a full five years ahead of the Russians.
The only thing you're missing is a parity with the Flanker entering service ca.1990 but you don't have that with the Eagle anyway (it's often referred to as a 4.5 gen even with analogue FBW). Flankers retain more of their design requirements in full service trim than Eagles do and have other benefits (STOL, low maintenance and rough field operation). But then again Flankers are made almost entirely out of titanium (brittle but very, very light for their size, fit and loadbearing).
The Eagle is supreme in 1970's air superiority, but the thing is it stands alone here. You could've done exactly the same thing with Phantoms with complete parity toward any potential aggressors. And the cost factor of achieving this, largely academic exercise simply cannot be understated. Seriously, the entire nation of the US would've noticed, really noticed the difference if projects like the Valkyrie, Blackbird and Eagle were never started. And the defence industry wouldn't have been any the worse for wear in terms of maintaining parity with national security threats.
It is after all, a "defence" force, is it not? Which is why many other nations would declare the US is just as bad as the Soviets in the Cold War role, and is more like Hitlerian/Stalinist rearmament planners than anything approaching a benevolent democracy. I mean what else if not an imperialist agenda? And this is being played out right now in the Middle East and central Asia at least to a foreign perspective, these oil wars and industrial imperialism (we want all the money, everywhere, and bow down dammit, etc.).