The F-4 was not that great a one-size-fits-all. It was supposed to be a standoff interceptor and long-range bomber. It was incredibly complex, and damn big. And we tried to turn it into a dogfighter. It kinda sorta worked, but there were far better solutions out there. The main restriction is that there are only so many spaces on a carrier, so you kind of have to make do with what you have.
The AF can get away with multiple varieties of dedicated aircraft e.g. F-16 for dogfighting, f-15 for long range interceptor/air-superiority, A-10 for ground attack etc. I have to think that the Navy tries to minimize the number of different aircraft varieties they put on the carriers, if only so there are enough of any one type to be useful (they have to carry ASW and helos and other things in addition to combat aircraft).
Also, isn’t the F-22 a dedicated air-superiority/interceptor similar to the F-15? My recollection is that it was never intended for the multirole activities the F-35 was supposed to take on.
Outside of land based P3’s and P8’s the Navy no longer have carrier based fixed wing ASW assets with the last S3 Vikings being retired in 2009.