Talking about myself, here. Or at least my plans for when I finally get some time to run my Gamma World/Marvel Comics mashup campaign.
Usually, I'm sort of easy-going when it comes to players rolling their ability scores. I let them make PCs at home, so they essentially get unlimited mulligans when rolling stats. What the DM doesn't know won't hurt him, right?
But in this new campaign, I'm thinking of taking a hard line. Why? Well, because I actually want to give players a choice of how they roll their stats, and need to be able to enforce it. I'm going to give my players a choice of rolling 3d6 six times and arranging to taste, or rolling 4d6-L (or with slight differences depending on character type) but in order down the line. This choice becomes meaningless if they just ignore the first set rolled and do it again, or roll both methods and take the better set.
Anyway, I'm thinking of possibly going so far as to suggest they tell me what PC type they want to play and which method of rolling they prefer and rolling the numbers myself.
Will the players revolt against this power trip of mine? Possibly. And I'll be the big softy I am and let them do it how they want in the end, because playing it their way is better than not playing at all. Besides, who cares if you've got an 18 Strength when you're facing off against a cyborg tyrannosaurus?