It might not be healthy for a character to labor with a very low ability score, but it's not unplayable. Like sure, if you have a Constitution of 3, you're not going last very long, but it's not like you can't rp being sickly and frail, coughing a lot, etc.., and even attempt to find a way to overcome that weakness.
People may not be super happy about having a 5, but I think people are happy that lower scores exist. Like, imagine if in some future edition, D&D got rid of scores below 8. So now 8 isn't "below average" it's the worst. Nothing can be worse than 8. Even children are running around with Strength 8 because the system doesn't support anything weaker!
(You can see a similar problem with the current creature sizes the game supports).
You could streamline the game by dispensing with these low scores. Just like you could streamline it by getting rid of ability scores entirely, as Pathfinder 2e and Fantasy Age basically did. But then you run afoul of people saying the game wouldn't "feel" like D&D anymore (rightly or wrongly), and that would have an impact on it's popularity.
That having been said, I think it's fine to limit super low scores on PC's just because you'll quickly run into some serious issues with the game- I don't think, for example, monsters are designed with the idea someone is actually running around with a 4 Constitution, to the point they'd have to roll a 13 to save against ghoul paralysis and their lifetime hit point total will be 60 points less than a guy with a 10...but YMMV.