They should roll their dice for their stats. That's what's fairer.
D&D, with all these options, is a tool kit for a DM and players to go through and use the ones appropriate for their campaign and not use the ones not appropriate. That's not arbitrary.
I'm having trouble reconciling your first paragraph with your second. On the one hand, only rolling dice for stats is fair (according to you, and using a strange definition for fair - if everyone being subject to the whims of chance is fair, how is everyone having the power to assign points to stats in the same way not fair?). On the other hand D&D is a tool kit and players should be able to decide for themselves what is best for their campaign. Interesting.
I am really getting tired of this "broken" claim. I can't say I've ever had much trouble with anything being "broken" in D&D. But then, I also work with my players to make the game work for everyone and I will expect my players not to disrupt the game with parts of the toolkit that do not work with it. I have some players who are definitely not min-maxers and the closest one I have to being one makes sure he doesn't outshine the rest of the PCs on a regular basis. And that works for us, as it should.
First, I'll hope you grant that it is theoretically possible for a game to include options that are so powerful that they are "broken".
With that assertion a given, we now design a single game with 2 playstyles in mind. 1) Your proposed style, where GM and players work in tandem with mutual trust to use only the options that further the goals of their game. I'll agree with you that this is the ideal. 2) A game where, for whatever reason, the mutual trust hasn't developed. Maybe everyone hasn't played together before, and the group is going through growing pains. Maybe they are all friends but have some pretty different ideas on what they want from a P&P RPG. Whatever. The point is, not everyone gets to play in an ideal group and we shouldn't punish them
even more just because they are unlucky.
If we include broken options in the game, it probably isn't a problem for playstyle 1. They work well enough together that they will recognize a problem and be able to fix it. This is how you claim your group works, and I compliment you for it. If we do not include any broken options, it is of course still not a problem for playstyle 1, though they'll have to find something else to spend their time houseruling.
For playstyle 2, however, including broken options is a big problem. It's a focus point for the preexisting differences, or maybe it starts misunderstandings that never would have happened with a more balanced, transparent system. Some people will be upset that they were tricked into "trap" options, others will object to their being able to swap them out because they should have to roleplay the consequences of their decisions. Things get ugly.
With no broken options, playstyle 2 has a much better chance to mature to playstyle 1 over time.
So why would we consciously ignore broken and trap options when designing our game? Removing them only improves it, even if leaving them in is fine
for some people. And, from a game designers perspective, blaming a player for taking an effective option is silly; if you knew it was a broken option, why didn't you remove it?