Different ability generation methods implicitly push for different playstyles. I absolutely think rolling for stats is a legitimate way of having fun, but with a caveat: It should be roll in order, and everyone should agree it's an OSR-style game where you don't get attached to your character much anyway. That way, the true joy of rolling for stats reveals itself in giving in to randomness and making do with whatever gets put in your hand. It makes rolling for stats an "oracular" process as Matt Colville once put in a video, and it can allow you to play characters you never would've considered otherwise. Having the Fighter with 1 HP be the sole survivor in a grinder dungeon because the player played them smart is a kind of fun you can only have when rolling for stats (and HP) IMO.
But, this is absolutely
not suitable for modern playstyles. People want to play capable characters whose character development is at least partially determined by them. They want to tell a specific story with a specific character, and they usually want that character to feel cool when it's their moment to shine. In order to have this in a group game, you absolutely need equitable (to use
@Maxperson's terms) ability scores, otherwise the person who rolled 2 18s and nothing below a 12 is going to do everyone's job, while the guy with 5 Constitution and no score above 14 will underperform (in a significant way, given how bounded accuracy makes even a +1 significant in 5E) in an unfun way. I absolutely despise rolling for stats when I'm a player, because my luck is not superb, and it feels like the kind of character I want to play is handicapped for no other reason than "because shiny math rocks deciding your character's baseline capability in an unequitable way is fun!". If unequitable characters in a gritty, hard-to-survive setting was what I signed up for, absolutely fine. But if I'm supposed to be wedded to a character for the upcoming 20-30 sessions and you will make everyone's capabilities swing by rolling for stats, that makes no sense.
That said, I think some methods of dice rolling can be equitable. I've found shared rolling systems where every player rolls one score and everyone shares the same scores to be fun while keeping the excitement for rolling. Similarly,
the 3-Up, 3-Down method presented by Jorphdan allows for variation in scores but mathematically ensures equitable results, so I think that's cool too. The stat draft presented earlier in the thread also seems like it would be fair. All in all, I think being equitable is really important in modern playstyles, so I usually just put standard array/point buy when I'm GMing, and insist on having some form equitable method when I'm a player.
