It is worth remembering that in Vietnam the AAMs were very unreliable, and USAF
pilots had done little air to air combat training, save for some against similar aircraft.
The AIM-9s and later AIM-7s improved in time, but when F-4Ds were first deployed they had the almost useless (for fighter vs fighter) AIM-4 Falcons, it took local commanders to remove them and put Sidewinders back on to change that.
In the Falklands Sea Harriers were fitted with 30mm cannon, but apart from the odd Pucara and helicopter, all kills were with AIM-9Ls.
It was not a great surprise to those in the know that they did so well, they had proved effective in exercises with NATO aircraft, including the USAF
F-5E aggressor units.
The Lighting was agile with a terrific power to weight ratio, it just suffered from not being updated and the design improved.
A well flown F-4 could hold its own against contemporary Soviet types, remember too that for the last 15 years of service, UK F-4s had the BAe Skyflash MRAAM, a much improved development of the Sparrow which has incorporated improvements based on Vietnam experience, as well as AIM-9Ls.
(It was an RAF Germany F-4M
in the accidental shoot down a RAF Jaguar in 1982).
But many of the RN
Sea Harrier pilots who shot down enemy aircraft in 1982 were RAF on exchange with the Navy.
The Tornado F.3 was for the specific mission of defending UK airspace and the Eastern Atlantic approaches from Soviet bombers, for that reason they were not deployed in the fighter role to 19 and 92 squadrons in RAF Germany.
I don't think it was a clever move to delete the gun from RAF Typhoons, however recent experience does suggest that it would not be used hardly at all in air to air, not against fighter targets at least, but if they wanted to reduce costs why not reduce the Typhoon buy to 230, from 232 aircraft, that would have covered it.