Why are special aircraft used for the carriers in the United States Navy?
It's technical, not political

The F-35 was an attempt to do exactly what you propose, lowering costs by planned sharing of 80% of parts across variants, but it turns out that the USN's F-35C costs over twice as much as the USAF's F-35A, and only shares 20-25% of it's parts. The project has been a disaster practically since day one, and the services are already working on separate replacements tailored from the start for their very different missions.

Per Wikipedia, the USN decided a carrier variant of the F-15 would be too expensive and the YF-16 was inherently not suitable for carriers, so they modified the YF-17 into the F/A-18 by making the changes you propose. The USAF didn't need those changes, so they stuck with the faster and cheaper YF-16, which became the F-16.

Keep in mind that all US aircraft carriers combined hold the fourth largest air force in the world. That sort of volume means the USN can afford to customize planes for their exact needs, whereas other countries with far smaller carrier fleets may be forced to make do with planes that the USN considers "unsuitable" or "too expensive", especially if they aren't US allies.