Okay, I'm WAAAY late to the party here (have been out of town) but wanted to add a note as a "food for thought" since I'm someone who has looked at the scores and statistics of PRS a fair bit.
At matches where mulligans were in play everyone who wanted to buy one did and the limit was 1 mulligan per shooter. If you bombed a stage you could pull out your mulligan and immediately reshoot the stage, then you keep your 2nd score on the stage no matter whether better or worse. The real question is... What do mulligans do to score distribution?
My thinking is that there is an element of skill to using a mulligan to enhance your score. First, you have to strategically use it at the right time... is this stage likely to be your lowest scoring stage? If you reshoot right now what are the odds that your score will be higher? Did everyone else around you score much better or did everyone just get equally wind-screwed? Second, there is some skill to actually being able to improve the score when you decide to reshoot. Can you diagnose why you missed and how to fix it right now in the 30 seconds? What are you going to do differently the second time around? Finally, there is a huge amount of mental toughness required in that moment. You just shot what might be your worst stage of the match, you're flustered, and now you need to perfectly execute the reshoot. This is why you often see people get worse scores on their mulligan.
While there is not data out there for this, I would strongly suspect that if you listed all the shooters who used their mulligan and ranked them based on the number of points they added to their score, on average the more skilled shooters would also be more skilled in "pulling points" out of their mulligan. And if this is true, then the net result is that mulligans would serve as a further separator of score distribution... resulting in LOWER scores on average for anyone who wasn't the winner of the match.
So my suspicion is that mulligans' effect on scores is probably the exact opposite of what people initially thought when they heard about them and raised them as an issue.
Disclosure: I shoot lots of PRS matches in the West where there are mulligans, I have bought mulligans probably about 1/3 of the time when available, and have used about half the time when I bought them. I voted against mulligans... not because of fairness or score distribution, but because I think they slow down match flow and because I prefer to see consistency rewarded - ie. don't mess up in the first place.