Keep in mind my point such a character is more a liability than a boon. If your PC is going to spend most combats on the floor bleeding out, soaking up the actions and healing that could be used to support characters who act actually fighting the monsters, I question why that character is there. The character OB1 and I discussed in 5e is minimally viable as a healbot, but isn't contributing meaningfully beyond that. If your joy is to be a walking, talking potion of healing, that's fine. But don't be too surprised if the other players stop wasting their actions to stabilize you after the 30th time you go down in round one to a fireball or critical hit.
Look, I can't convince you that playing a character with all 3s isn't possible. I'm saying though it's not the enjoyable experience people who advocate for rolled scores say it is. If it was, Gary wouldn't have wasted space creating 12 alternative ways to generate ability scores in the DMG and UA, one of which becoming the default method in all subsequent versions of rolling (4d6).
All I'm saying is if you play a character that sucks and can't contribute meaningfully, don't be surprised if I don't waste precious resources to save them.
I also want to briefly hit this from the other side. A game I am currently in we all rolled for stats, and we all rolled GODLIKE stats. After the +2/+1 my character is sitting at a 16, 16, 16, 13, 19, 12 and I know another party member
started with at least two 18's before the mods, and I think currently has two 20's.
We barely notice.
Legitimately, we are not running around like gods among men. I've occasionally referenced my character's unusually high strength for a cleric, and I've taken advantage of having a decent dex score since I'm playing a trickery cleric and ended up defaulting into being the rogue of the group, but none of us feel we aren't challenged or that the game is too easy. Heck, we nearly TPK'd in our last fight.
I know people are going to claim that this means we wouldn't notice the low scores either, but that's actually wrong. I've played in games with someone who decided to play with consistently low stats... and we all noticed it. We were very aware that they just had a worse chance of success than most of the rest of the party. They did consistently fall short, their spells did consistently fail to land. In another game we just had our sorcerer one-shot because at level 3 they have only 14 hp. They rolled a crit to avoid being kidnapped and warned us of an ambush, then was instantly dropped before they could do anything else. No one else in the party is that fragile, including the wizard.
I know it seems counter-intuitive to people. But a 16 seems to be the pivot point in the math. I've seen multiple characters who had multiple scores above that number, and other than the occasional "oh, the wizard broke down the door... neat" it is hardly noticeable. And I have seen multiple characters without a 16 in any score, struggle and grasp at straws to not burden the party. Yes, it is a one point difference, but it seems to actually matter to the math of the game. Maybe it is just my games, maybe it is just my sample size, but it does seem to actually make a significant difference. And a character with no score higher than 10? No one is interested.