I surfed WikiPedia briefly and got the clear impression it wasn't so much the range of the RN (Sea Dart) SAMs which was the problem, so much as their radar's inability to lock onto wave-hopping aircraft. Apparently - despite being a fairly short-range system - Sea Dart racked up a very good record at altitude against all Argentine aircraft - downing even more of them than claimed at the time - but just couldn't lock onto surface-skimming attackers. (So much so, that in the later engagements they apparently took to firing them off, unguided, for whatever distraction effect it might provide.)
Interesting that, fully 20 years (at least) after their first development, when put to the acid test of actual combat, shipboard SAMs proved still incapable of full anti-air protection - not against real, thinking human-beings at the controls, anyway - even when those aircraft were the very same, by-then obsolete models dating from those same two decades earlier! The above would appear to explain the obviously heavy emphasis on radars, in the decades since - notably on the Arleigh Burkes and (especially the) Aegis cruisers.
And it makes you wonder seriously how all the latest systems - clearly by now far more complicated and seemingly dicey than a simple, radar-guided SAM - really would hold up, in an actual, conventional-war sh**-fight, today. GPS in particular, it seems to me, remains a weak and highly vulnerable link: take out (probably less than) 10x of the right satellites - either with ASAT missiles or just a couple well-placed nuclear EMPs, out in space - and it seems to me all the "smart" bombs, drones and who knows what-all else will then just begin to wander aimlessly, and/or fall to the ground. These things have never proven themselves combat-capable and in fact only "work" because they are being deployed (>95%) against utterly defenseless civilians.
Which, of course, is the real problem with these latest-generation weapons: our So-Called "leaders"...