I absolutely do not enjoy big random in character essentials for long games. If it's a one shot, fine, I'll have some fun with the 12 int wizard or the clumsy rogue. I don't want to be stuck mechanically underpowered for months, maybe years, due to the whims of a tiny portion of dice rolls.

As for "but flaws make interesting characters", yes, but there are systems that do it so much better. A character's Trouble in Fate, or dramatic failures in CofD come to mind. I've ported both of those over to DND and it worked fine, so you don't even have to change whole systems.