You're missing the point entirely. If we wanted to, we could put an F-15 on a carrier. In fact, there were two variants developed. The only reason it didn't go through was because the Navy was already committed to the Tomcat. But you can't put a Raptor on a carrier. It's physically impossible. The F-22 can't go slow enough to land on a carrier, it'd rip the cabling and probably crash into the sea. Furthermore, carrier planes are designed to be more rugged and require less maintenance, the exact opposite of what the F-22 is.
What wins in dogfights is superior situational awareness. Superior situational awareness requires not only having good situational awareness yourself, but denying it to the opponent. What this means is that aircraft must be capable of detecting and identifying the enemy completely passively. Currently, IRST and optical sensors are only types of sensors, except for Mk 1 eyeball, to posses such capability. F-22 lacks both, and as such has to either have an uplink to another platform – and such uplink can be detected and jammed – or to carry out both tasks World War II style, with pilot doing detection and identification visually. While F-22 was supposed to have FLIR, it was deleted as the cost-saving measure, and there are no plans to fit it.
Moreover, while some measures have been taken to reduce F-22s thermal signature, no major reduction was (or could have been) achieved, especially from the front. F-22 is also very large, increasing its detectability by the IRST. Thus, F-22 will be easily detected at ranges exceeding 80 kilometers by opponent using QWIP IRST.
Modern heat-seeking missiles also do not have to rely on engine exhaust for locking on the enemy aircraft, but can rather lock on to aircraft itself.
F-22 also isn’t undetectable to the modern radar, despite what some accounts say. While F-22s RCS of 0,0001 and 0,0014 m2 reduces detection range considerably, Typhoon’s radar (which has detection range of 185 km against 1m2 target) can detect it from distance of 18 to 35 kilometers. On the other hand, modern RWRs can detect LPI radars from ranges two or three times greater than such radars can detect target with RCS of 1 m2 at, thus making any use of radar an unwise course of action for F-22 (and any other fighter aircraft).
The difference is that neither Russia, China, nor Iran have made any indication they want a full stealth air fleet as far as I know, whereas the USAF has indicated that's exactly what they want.
Lol wat
Washington used aggressive sales pitch to sell F-35 fighter, memos reveal
Except no.
BVR combat is a pipe dream.