Why? Tabletop RPG games (yes, that is what I mean with D&D considering that was probably the most influential tabletop RPG games and pretty much defined the genre) even include such things in many cases. It usually is reflected by a loss of some stat, such as strength or agility. And, as you pointed out, a major part of RPG games is role playing. If you completely ignore a broken or missing limb, how would that be role playing? You can, of course, have some kind of special training as part of the game that can let you overcome such a weakness, but having that impact your game fits well with RPG games.
If the majority of people consider it to be true, they aren't wrong. Especially considering it is an opinion, which can't be right or wrong. You may not like it, but they aren't "wrong".
The player, not the character. If I break my arm, it shouldn't effect the character I'm playing in the game.
...that's not true at all. At one point, the majority of people thought the sun revolved around the Earth. They were most certainly wrong.
What does breaking your own arm have to do with anything?
He was making an argument against "action mechanics". His skill at a mouse shouldn't be a part of an RPG. => His character is separate from his flesh.
