Quali is a waste of time for public races, IMO. It takes too long to organise for the amount of people and laps. Also, some people may be "safe" but slow, and if midrace join is enabled..
The training system might work though, and nobody would have to do it every time, if the progress status is stored on LFSW (or w/e, i.e. not on the user's PC). It would have the advantage of 1) allowing all the combos to be driven in LAN and SP 2) not allowing utterly dangerous drivers online 3) not having to do the training things every sodding time your PC dies on you.
But the training content would have to be objective, interesting, not time consuming, be aimed at driver attitude as well as technique, etc.