DM answer to this: you'll not be taking up game time rolling up your next; instead we'll get together during the week and see to it then. (never mind that it'll inevitably be that low-Con fighter who survives the longest!)
Ideally as DM all characters are rolled in front of me but at roll-up night when everyone's rolling at once having another player observe is fine.
That's what pre-roll characters and promoted hirelings are for. No lag time. "You've been making fun of Tim the lantern-bearer for the last year, now he's your new character. Go."
but why make them play a character they don't want to?
Lets say I roll 9, 9, 11, 12 ,12,13. I look at 3 +1's and and 1 - and 2 -1s and say "I don't want to spend the next X months playing with that"
why not just let me reroll?
Is it really BETTER to have my character (9str 11 dex 9 con 13 int 12 wis 12 cha) played and not enjoyed?
I think the point that's being missed is that it's a game. The point is to have fun playing it. Is your definition of fun only getting exactly what you want? You only have fun if...and only if...you get to play exactly what you want. That seem bizarrely limited.
A few relevant quotes form older editions...
“The D&D game has neither losers nor winners, it has only gamers who relish exercising their imagination. The players and the DM share in creating adventures in fantastic lands where heroes abound and magic really works. In a sense, the D&D game has no rules, only rule suggestions. No rule is inviolate, particularly if a new or altered rule will encourage creativity and imagination. The important thing is to enjoy the adventure.”
And: “the object of the game is to have fun by playing roles, stupid or weak characters can be as much fun as smart, powerful ones—if the roles are played well.”
In my experience, players given the chance to simply pick their stats would have all 18s across the board. They seem to want to play perfection and anything less, even the hint of a negative or a flaw is anathema to them. It just seems backwards to me to decide you can only have fun if you get exactly what you want. Instead of see what you get and have fun with it no matter what. I mean, I just don't get that attitude.
Player: "I want to play a goblin artificer and I refuse to have fun or even play unless I get to play exactly that."
DM: "I told you we're playing a low-magic humanocentric game this time. Instead of the 12th generic high-magic fantasy romp."
If the player wants to die on that hill and not play at all, sure. But that seems like an incredibly...silly choice to make. I just don't get the attitude that if you can't play something super-awesome you'd refuse to play at all. General you, of course. Not trying to specifically call out the posters I quoted.