FWIW, I have done some data mining on this topic when we were on the same tire and found that, at least in NorCal, the NASA -> SCCA crossover is significantly smaller than SCCA -> NASA. Therefore, while an attractive theory about being on the same tire, it is not one that seems to play out in our neck of the woods.
I think that's probably the same story for most areas, as the SCCA is much more racing focused than NASA. Given that, having the same tire will reduce costs for some percentage of the population. This benefit needs to be measured against any benefit derived from spec'ing a given tire. Service at the track, contingencies, kickback to the leaders are all part of the equation.
Here's an alternative. If the tire of the "alternate" sponsoring organization is less competitive, why not allow it? For last year, would anybody have complained if the RR was run in SCCA SM?
I guess there might be some track, under some conditions, that would favor the lesser tire, but that's the complete outlier.
For the case of the SM6 vs the RR, this may have gained attendance at SCCA events as the SM6 seemed to be the tire of choice.
I'm sure there are exclusivity deals that I'm not aware of that drive the equation, but I'm just a racer.