Right. So remove this one constraint. Why does the point buy, die roll, and standard array need to stay as a constraint? You are removing one constraint out of a hundred. The player still has to pick a limited number of skills. They still have a limited number of weapons to choose from. They still have a limited number of spells. They still have a limits on their armor. They still can only choose one archetype. They still have to choose a single feat, even though they may want three. They still have to be constrained when choosing armor. And the cycle repeats itself over and over through the levels.
So why have the constraint there when it causes so much debate?
I just don't think you are comparing apples and apples.
Yes, there are lots of different constraints in the game. One is in how you choose attributes, and another is where you put your attribute bonuses.
In my mind (you may disagree) the one about the attributes is a matter of balance. If players pick their own scores then either challenges get too easy, or the DM has increase the challenge. But since different tables will have different behaviors, it would be very hard to write published adventures. So a fixed system of attribute selection helps balance the game.
The fixed ASI rule has absolutely nothing to do with balance. It's about tradition. Getting rid of it doesn't (or shouldn't; it's possible there's an exception case I haven't considered) cause any other parts of the game to work less well, to change in any way. The only opposition to it is one of perception.
So maybe "pick your own attributes" is a great idea, and we should open a thread and discuss it. I'm not saying we should dismiss it out of hand, I'm just saying that it's not really valid to compare it to getting rid of fixed ASIs.
If you want a valid comparison, pick something that is about tradition and flavor, not balance. "If we get rid of fixed ASIs, why not get rid of druids and metal armor?" (Which has been mentioned in this thread, although it does have a tiny balance component.)
I'll point out that they
did get rid of the requirement that Paladins be Lawful Good, which was a constraint that served no mechanical purpose. And some people were/are upset about that. They
did get rid of gender-based ASIs, which was a constraint that served no mechanical purpose. And some people were/are upset about that. I'm sure if I were to keep thinking I'd come up with more.