Your argument that the airlines "need" GA to give pilots the essential old-school stick and rudder that they need, is, I'm afraid to say, a complete load of baloney
It's a long time ago but I clearly recall the contempt shown to me by two GA operators when I applied for a job with them following my retrenchment from an overseas 737 operator back in the 80's. Sent a modest CV (one page) to Kendall Airlines in Wagga, followed up by a short phone call to Don Kendall the chief honcho himself.
Informed I was ex RAAF and ex airline, he told me bluntly that he would not embarrass his young captains by having me in the RH seat and furthermore at my age (45) I wouldn't have the strength to lift the bags into the hold. I had the impression he had a real dislike of RAAF trained pilots.
Similar attitude when talking to the deputy chief pilot of an MU2 operation at Essendon. As soon as he saw the same one page CV, this character said thanks - but no thanks. I asked him what was the problem? He said as a former RAAF pilot I wouldn't have a clue about flying single pilot IFR and in any case I would expect too much of aircraft serviceability in GA. In other words he required pilots who would be happy to fly a defective aircraft and say nothing.
Since both these events happened within a few days of each other, I can tell you it was not a pleasant and fulfilling introduction to the world of general aviation in Australia.