Variety adds to realism. I'll give you that.
When playing Monopoly (a typical board game) no-one expects you to create an alternate character to role-play, and wonder if the particular capitalist pig you are playing this time is the kind of guy who would bulldoze four houses and evict the poor tenants just to build a luxury hotel for the bourgeoisie!
You are not playing a character; you are you, trying to win a boardgame according to the rules of that game.
Part of the rules of that game are that each player starts with the same amount of money. No-one expects to have a random roll to see how much money they start with, because realism has absolutely nothing to do with the game.
The 'move rate' for each piece is 2d6. Why can't the car go faster than the old boot?
Because you are not pretending to be a car or a boot! They are meaningless playing pieces.
But if we were DMs trying to create a believable world in which to have adventures, then it would be totally unbelievable for each person to have the exact same amount of money. That every entrepreneur has to receive the exact same 'starting' cash from Daddy (as if everyone 'starts' at the same time!), and their natural talents are divinely mandated to be equal.
So we have a spectrum: at one end is the 'just a game, therefore everything
must start equal' attitude of a mere boardgame. On the other end is the 'reality sim' attitude.
Since our hobby is
both 'role-playing in an imaginary world' AND 'a game', then we each have to decide where our table is on that spectrum, and we have different tastes.
For those of us who hold 'realism' as more important than 'only a game', then 'realism' is more important than 'fairness' in character generation. Therefore, rolling is more attractive than point-buy or standard array.
For those of us who hold 'only a game' as a higher priority than 'realism', then a fair/balanced PC generation system is more attractive than one with realistic variation. Therefore, rolling is less attractive.
One reason that this thread is so long is that human nature leads us to treat the way we like things as the way things should be, and find it weird when we see people making the opposite choice. I see people who treat RPGs like a board game and my knee-jerk reaction is that they are having fun wrong. I don't get it. It seems to me like they are throwing away the best part of this extraordinary hobby just so that they can play a rather complex boardgame, whereas right-thinking people like me get the best of gaming AND role-playing in a believable world.
Of course, I realise that it's okay for other people to like different things. But I still don't get why they want those particular things.