In my Light Against the Dark campaign, I had the players roll the character's ability scores, 4d6/drop lowest, in front of me. I did this because it was reasonably fun (in a shooting craps kind of way), the results were interesting, and it forced the players to take a sort of "will of the gods" approach right from the start in a Grecian Gods kind of campaign.
And it was D&D, right? I have some unresolved nostalgia issues

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But nowhere in that list of reasons to do it was "fairness" or "play balance". When I want "fairness", I negotiate with the players for what method both they and I will be happy with. When I want "play balance", I laugh heartily and go hunt other, easier-to-find mythical beasts, like violet, winged half-dragon unicorns.
Most of the time, I just let the players use the system to describe their protagonists, after I give as thorough a description of the power level/competency level I want to run the game at. For example, in the Book of Runes campaign I'm running right now, it's semi-pulp adventurers who are wealthy, experienced, and certifiably crazy to be doing the sorts of things they do. So the players picked one or two strong talents to define themselves with, explained their skill sets to me, and off we went.