While the J101 was under-sized for the Phantom, the engine core could have been upsized into a J79 thrust category.
That's essentially the genesis of the F404...
GE15 designed for export fighter category (circa 1969) up to about 10,000 lb thrust
-> Evolves (and "steals" CF6 combuster design elements) and gets a new name J101 to support Northrop projects including YF-17, eventually getting up to 14,000, then 15,000 lbs
-> upsized fan with J101 core becomes F404 With 16,000 lb thrust, eventually/currently 19,000 lb thrust
-> nonafterburning, much larger fan F412, new material advances, heavily modified (~13,000 lb dry thrust)
-> smaller (than F412) fan, shortened and substantially modified compressor and combuster gets to ~18,000 lb thrust, improving quickly to 22,000 lbs thrust, still being tinkered with
Yeah, the F404 was an almost perfect drop in replacement for the J79. I'm honestly surprised that no one opted to do that with their F-4s...
So the same or better thrust at lower fuel burn ...
The F404 works as a J79 replacement because you have the same thrust for less weight and space;
The early F404, including the first 1,000 or so production Hornets, had almost 2000 lbs less thrust than a J79 (though fewer parts, less weight, etc). Phantom is twin-engined, of course, so you're asking a customer to cut 3800 lbs of available thrust from their Phantoms. Everyone wants
more thrust, not less, from their Phantoms, by this point (PW1120 proposals from mid-80's).
The more powerful F404-GE-402 gets to essentially thrust-parity with the J79 (considering weight differences), but by the time it's ready for prime time and is ordered into production by the USN, we've made it to very late 1991. Most everyone has moved on or isn't willing to invest the money. ICE, starts almost a decade earlier in 83, for example, and is aimed for interim roles until replacement (of course, the Eurofighter is repeatedly delayed, so the Phantom stays on longer than expected).