I hope that some one has already done the analysis
Over a decade ago all sorts of options were looked at; options for the aircraft and options for the ship/equipment. The fact that Rafale had been tested with a ramplet on the end of the catapult was not ignored. Neither was all the UK corporate knowledge of ski-jumps in general. Nor, indeed, was a completely blind eye turned to US studies. Too much like hard work to ignore what the Russian Navy was up to as well. The net for options for getting the aircraft back was also, initially anyway, very widely cast. Quite a lot of in depth 'looking at' was done actually.
As well as this of course, sight was not lost of the purpose of these aircraft which is to go places and look at and if required 'influence' stuff. In other words, launch and recovery is not what you buy the things for or employ pilots for, except as a tedious necessity. Not surprisingly, some time later, an invisible aircraft that was cheap to run, trivial to launch and recover from anywhere (in conditions including 'not great') and needed the cheapest ship was chosen.