Even better (in theory) would be to have these tyres being compounds that are not used in the race. Different tyre sets for qualifying and race could be one way of assuring that cars don't line up on the grid in order of race pace. Also, it would throw up an interesting strategic dilemma for the teams, as they'd need to balance competitiveness in qualifying vs competitiveness during the race through the FP-sessions - almost certainly not being able to optimize their cars for both instances.
Don't think that this is practically feasible though, as it essentially would require Pirelli to bring six different compounds to each race, well well...