In my book, I don't view dice rolls during play and during character generation the same. I view the latter as gambling with your character. In game, a dice roll represents a single action: swing a sword, pick a pocket, resist a spell. The odds of that one roll permanently affecting your character is small. The attack fails, but the rest of your attacks aren't affected. Plus, those rolls often have modifiers that influence them like ability bonuses or level bonuses (ThacO/BAB/PB).
Whereas ability scores generation is permanent. Those six rolls will stick with your character for their entire play. A bad roll here cascades to all future rolls with that score. Depending on edition, you may not be able to fix it without DM intervention (magic items and boons) or have to use multiple stat increases just to get to acceptable. Further, there are far less ways to weigh the dice favorably. An extra d6 (drop the lowest roll) being the only one, assuming you are picking a race for any reason other than the ASI.
So my rule is short term uncertainty is desired because that adds drama to the game, but long term uncertainty is bad and should be avoided. Things like ability scores and hp are too integral to be left to a single roll. (I mean, we don't roll to determine starting level, or roll to determine AC or attack bonus, but we do/did with AS and HP?)
