The RN Sea Harrier pilots, I imagine, stuck to their forte, shooting things down, not that the R.A.F. didn't have anyone capable of shooting things down, just that their expertise was doing so with the afore mentioned Lightnings and Phantoms.
Oh, a PS for you, why didn't they station Sea Harriers permanently in the Falklands? Why Phantoms?
Wasn't the demise of the big carriers in the 70s in part to do with an Air Force claim they could defend the fleet anywhere in the world?
Having once again proved the flexibility of VSTOL, the SHAR and GR continued to provide air defence until three months later the less flexible conventional fighters could finally defend the fleet, oh sorry, the Islands.
Why would they permanently base a fleet asset on a land base?