I find this a bad reason for random character stats. The world is already stacked against people, I already know how to live in a world of rampant inequality. Perhaps I want to play a game where those factors are exacerbated. We don't roll a d20 to see what level you begin as (despite people coming from all different levels of experience) for example. We don't play Monopoly with each player starting with different amount of wealth and property already (despite the fact that would better model the economic advantages some people have). We assume an even playing field.
A 5'2 person can't play in the NBA, so he won't try. It's not like they are going to show up on draft day and find out they can't play after being dunked on by everyone. Realistically, all those quirky "low score" characters (the ones on the low end of the bell curve) would realize adventuring requires gifts beyond them and likewise take up a mundane profession. Ergo, most of those "low roll" PCs should retire upon creation unless they are narcissists or non compos mentis.
And on those odd occasions you do have the protagonist that isn't gifted defying the odds, it usually comes from some external factor: wealth, connections, magic, or good luck. D&D offers no plot armor of this type though, there are no mechanics to balance low rolls with other bonuses. It is uncaring that you rolled poorly on ability scores, HP and starting wealth.
And in the end, I find that a flaw rather than something to be celebrated. I already live in a world where those who are born of privilege, be it economic or genetic, have overwhelming advantages all under the guise of a meritocracy. You're going to have to forgive me if I want the fantastical concept of equality in my silly elf game.