Steve,
i'm not going to give my opinion on whether or not coaches/instructors will require a belly pan but for the sake of argument:
I won't go into detail, there are many rules that are bent throughout the weekend for the sake of allowing people to get track time and ride. At the end of the day, the club wants less babysitting and more racing. it has to go both ways. this is a trust thing. there will always be exceptions to the rule, regardless of how many times someone will tell you otherwise.
The club can easily go the other way and spend more time at tech ensuring every nut and bolt is properly snug and wired in a way that provides positive locking force on the nuts and bolts. double check everyone's fluids, be nit picky about tire wear, etc. this will result in longer tech times, frustrated exec, frustrated riders, less track time, etc etc. the onus of a mechanically sound and properly prepped bike is on the owner, not the club.
I don't think anyone wants to show up at the track at 5am just to make sure everything is tech'd and ready to go. should we re-tech bikes that have tires swapped too? the list is endless if we want to scrutinize the small things.
The Hoff:
as for instructors crashing, the last 2 race schools I am pretty sure both had instructors crash at speeds that were easily out of their pace. pros make mistakes too. dialing it back can cause someone to be complacent and that's where accidents happen