WEBF, while you may be right that the carriers were essential without a rematch without carriers we cannot be certain.
Certainly the timescale would have been different. The method would have been different and the force composition would have been different.
Without going back too far, ie we would have had X more frigates if we had no carriers, you could re-examine force levels available. Maybe the SSNs would have been employed differently. Maybe we would have operated the Harrier from merchant men etc.
It would make for an interesting table top exercise to run the same scenario, same ship availability less the carriers.