It absolutely is, if you don't get exactingly hung up on numbers, and do consider that others will be playing the same game.
So 'point-buy lets people play the concept they want', does it? Let's look at
your own arguments intended to demonstrate that:-
Under point buy, if you want to be the big dumb barbarian, you dump a lot of points into STR and dump INT. Unless you're hung up on numbers, that's letting you play the character you want. Now, depending on the details of the system, you might well get an even higher STR and even lower INT rolling randomly - you also might roll a low score of 13 and high of 15, and come nowhere near it.
It lets you play the character you want
if you want the strong-but-dumb barbarian, but does
not let you play the equally strong but
smart barbarian! In life, you can get to be stronger by lifting weights, exercise, that kind if thing. In point-buy, you get stronger by banging your head against a brick wall until you lower your intelligence!
Look around you. In real life, people are not made equal. If you were to assess every adult in terms of D&D ability scores, they would not all add up to the same points total; far from it!
Even our celebrities, even our figures from film/TV/books are not churned out of a machine that ensures 'fairness' in ability scores.
Now, I grant that 'balance' has its place, and how valuable balance is depends on the game. But in terms of realising concepts we want to play, the smart, charismatic 'noble savage' that's just as strong, tough and agile as any barbarian (like Tarzan) are perfectly valid concepts, and point-buy will not model that.
Dwayne Johnson, The Rock. What's his Str score? Dex, Con? Right up there. That doesn't leave us with any points left over for Int and Cha. But The Rock is both smart AND charismatic, and he doesn't become weaker as he gets more charismatic! Quite the reverse actually; his physicality is part of his appeal.
The Rock, or a hero like him, is a perfectly valid character concept.
But point-buy will. Not. Do. The. Job.
That doesn't mean that 'point-buy is worse than rolling'. It doesn't mean that point-buy has nothing going for it.
It just means that the claim of 'point-buy lets you play the concept you want' is untrue.