Sorry, but it's clear you either don't know enough about the situation or haven't read the previous posts, and those on other forums.
The French and Italians deployed carrier aviation, but as a small part of their overall effort and it was not by any means critical to the effort. It wasn't "ideally suited to the job", or there would have been some observable difference between what we got out of carrier-borne air and land-based air. Actually, there wasn't.
If you think that TLAM could have done the job of Storm Shadow, clearly you don't know enough about the weapons. The USN fired something like 102 TLAM on the first night, but the USAF still needed to drop several times that many bombs, and Storm Shadow was required as well - TLAM has a comparatively small warhead (just under a 500lb yield) and no penetrative capability. It has basically no capability against bunkers and other hardened targets.
I would very much like to have kept the Harrier in the RAF inventory, but even if we had been able to afford it it would not have replaced the capability provided by Tornado and Typhoon. Don't forget that Italy deployed AV8s on Garibaldi - and frankly, they didn't bring much to the party. Always difficult to measure, but it is clear that the Italian Typhoons contributed more than their AV8s.
If you wanted to spend a fraction of what we paid by sending a carrier, the implication is that we would not have deployed out AAR, AWACS, Sentinel, Nimrod R1, comms fleet, ISTAR ground facilities etc etc. You are deluding yourself if you believe you can run an air campaign from a carrier - even the US wouldn't do that. Focussing on what fast jets provide is the mark of a rank amateur in air power terms.