Part of the reasoning behind ASRAAM integration on the Jaguar was that it (partially) enabled a self escorting strike capability, given that proper fighter escorts might not be available. It worked for the Jag. In (simulated) exercises it performed well and as I recall even got Typhoon kills. My argument is very simple; a radar less aircraft with Sidewinder is likely to generate a Martin Baker tie. The same aircraft with ASRAAM with a LOAL capability is going to be much more effective. That means it would have worked better from any platform, land or sea.
Putting a sqn of carrier based GR9s with ASRAAM would have generated a very useful capability in a Falklands or Gulf scenario. In the Falklands most kills were visually acquired. Having a long ranged, very fast IR weapon is highly desirable and much more effective. Does this make it a fighter? No of course not, but I believe it would have transformed the very limited capability that the GR brought to naval operations.
I wonder if any ex-Jaguar operators would care to comment on the difference it made.