...but would a good F4 keyboard warrior actually be able to fly a F16?
Based on my experience, absolutely not.
Being able to take off, fly, land, and fight for years in P-51's, F-16's, A-10's, F-18's, and a C-172SP on a computer got me < 5% of where I needed to be to take off, fly, and land a real C-172SP.
Take off and flying are probably the easiest and the most likely candidates for having Flight Sim skills transfer over. Landing is a whole different story. I find landing a C-172SP in FSX really sterile, bland, and boring becuase it is so much NOT like the real thing. Landing in real life if hard. I could have greased 300 landings in a row in FSX and still would have killed myself on the first real life C-172SP landing.
Of course, my experience is based on a C-172. It's possible that flight sim skills transfer over more in something like an F-16, where a computer is more involved in the actual flying anway. Or maybe they transfer over less. I don't know.