I've conducted lots and lots of airtests and have never had a problem at Vne. The provisos are, however, it should be approached with caution (you don't need to accelerate straight through it, just a short visit will do) and this should be conducted in smooth conditions.
More likely that the aircraft dropping to bits at Vne is that the pilot will have forgotten to retract the flaps after the stalling sequence! This has been done before (not by me though) leaving some very unwell flaps.
The simple fact is that the airtest is designed to examine the certied range of operations of the aircraft - something which could occur in normal operations. Sounds like your Cub might need some attention with the aileron rig?
Why is it 'bizzarre' to operate an aircraft throughout it's normal operating range once every three years?