The numbers mean something to me - If I play a RPG, I want to use the numbers that define my characters because they represent this character. If a session never requires me to use any of my character abilities, I feel a bit like I wasted my time, or at least didn't really play that character. It was just me, thinking about a fictional situation and reacting to it, and the person I was impersonating didn't matter.
But that's not enough, sure. I also want to feel challenged myself - by choosing which character abilities I use, and how. In combat, these are tactical decisions - which ally do I aid in his attacks, which enemy do I take out first (and how), which ally do I protect, how can I maneuver my opponents into a situation more favorable to me.
Well, "magic" is not realistic at all, and yet we want it in our fantasy games. My view on this is that a role-playing game is still a game. Imbalances are not a sign of a good game. In reality, someone trained in using a gun might be a lot more deadly and survive a lot longer than one with just some martial arts training. But in a game that includes both options, they should be equally valid (assuming equal cost, yada yada

).
This is not a simulationist perspective, I suppose, but I find the "validity" of all available roles in a role-playing game very important for my enjoyment of the game.
There are other gameplay concerns for this - I like having the ability to make "fair" challenges for my PCs when I DM. I want the ability to predict how tough any situation (be it a combat encounter, or anything else that will resolved with dice) will be for them. A game that doesn't ensure balance across the board makes this very difficult.
But I might be willing to compromise here - if an individual class or character is not good at certain situations, give me tools to handle this difference. If a Noble is inherently inferior in combat to a wizard or a fighter, give me a number that describes this difference so I can take it into account. If a Fighter is inherently inferior in a social situation then a Noble, again, tell me how much so, and I can take it into account.
I still find this inferior to using balance across a board (to be expected by a compromise), because it still makes it likely that one or more players will not enjoy important parts of the game as others, simply due to their choice of character.