FL,
Having experienced working with a SMS as both mil and civ I agree with you. I'm not sighted as to whether the large display operators run an airline style SMS, but if they don't perhaps they might adopt one. Although very time consuming, a SMS based on SIRAs is a powerful tool for identifying risk, and putting appropriate barriers/mitigations in place. With an SMS endorsed by the CAA perhaps FDDs would have more confidence in hiring aircraft and staging displays?
My concern would be the 'one man bands' who own/operate a single/small operations. A proper SMS requires a number of honest inputs, and the outputs can drive expensive solutions. It might be the final straw for some.....