One of the problems is that the pilot may not know the reason why the bit of kit is there in the first place and this, often, is a straight certification reason.
Thus, if you go with it busted and no MEL or similar permission, then you have compromised the certification basis for the Type and, sequentially, invalidated the CofA for the aircraft.
Best have a very good story for the inquiry if it turns to custard ....
Looking to stall warners, for instance, they are there, generally, because the stall characteristics are deficient in some respect ... the old story applies .. you can fool all the people some of the time etc ... but, every now and again, the chickens come home to roost with a vengeance and you may have egg on face syndrome and a difficult time with the coroner/police and the insurance company.