Full time refs would be under further increased pressure - pressure to get decisions right and explain the decisions they made. Remember they are making the decisions quite often in a split-second and don't have the benefit of seeing a replay. IMHO it wouldn't be a good idea. RiG - you're a fit young chap. Ever considered doing the course and taking it up?
In seriousness though, the SFA are actively encouraging more younger girls and guys go in to refereeing. I don't think the problem is with the refs per se, but more a case of the pressure placed on them. To hit Cat 1, you need to work up through the ranks doing juniors and u18 games etc - quite often on your own. Because there is so much pressure on players from parents, coaches etc this affects the behaviour both on and off the park. Of note, the physical aspect of the SFA requirements are far more stringent than UEFA.
I don't think young players should be joining clubs at such an early age (as Gabby says 10 years old). They should be allowed to enjoy the game and playing it. If this pressure was removed from their shoulders, then the pressure on the refs would lessen and we would have a larger pool of refs to rely on.
Another major factor IMHO is the behaviour and conduct of SPL players and coaches / managers. Youngsters look up to them as role models and emulate their behaviour and actions. The change does need to come from the top I think. I even noticed a tweet today from The Sun newspaper stating that "Neil Lennon is ready for battle against Hibs on Saturday". Sorry, it's not a battle Neil. It's a game of football. A game.
The sooner people realise this, the better. What I'd suggest to anyone who goes to a football match (perhaps a lower league game or even a game at the bught) is to watch the referee and compare them to the refs who do the SPL games. It's a tough shift. Don't knock it until you try it!