I've been lurking on this thread for quite a while, and have been surprised by how few people seem to actually like rolling for stats, but even more surprising is the sentiment that having unbalanced PCs is bad for the game. I'm going to dip a toe into the conversation, and I hope, bring some new thoughts into the nature of the disagreement.
D&D is in the Fantasy genre, which tends toward stories about having the power to control the world around you and about being the chosen one who is destined to save the world via your power. Hence the concern by some that by being underpowered, you are relegated to the "sidekick" role and thus not participating in the game the way it was meant to be played. Point buy and Standard Array help to alleviate the disconnect between the genre defined need of a singular hero with the fact that this story has several "main" characters.
If however, the game is approached from a team sport perspective, the expectation for balance begins to change. Everyone isn't expected to be able to contribute at the same level, but that the contribution of everyone to the best of their ability in their role leads to the success of the team. One doesn't have to be the leading scorer on their team to enjoy playing, and is likely thankful to have someone of great talent to help them win.
I do think that the method of character generation needs to match the goals of the story. Are you an elite force assembled to battle a great evil? Point Buy is probably the way to go. Are you a group of misfits who came together by necessity and thrown into events? I think rolling leads to more interesting results.
By dismissing one style or the other, you are shrinking the toolbox you could be using to tell a great story. I see both as having a place.
For what it's worth, when I do have my players roll stats (as we have for YP), we don't just roll abilities, it goes.
Roll 4d6 drop lowest in order
Roll for race
Roll for background
Pick class (Per the PHB, your highest stat must be in the prime requisite for the class)
For us, the random results of this lead to unique characters and stories, as well as a different kind of challenge.