I think you are talking about two different kinds of balancing:
1) There's balancing the different cards against each other, and
2) there's trying to create a balanced game for two players by giving them equal access to the same options.
Sure, but the two sorts of balance turn out to be inextricable. The pieces of the game have to be balanced against each other, and the access to gameplay provided to all the players has to be balanced. If the pieces of the game aren't balanced, then it tends to reduce access to the gameplay for one or both players.
Adding Chuck Norris clearly breaks 1), since no existing card can compete with Chuck Norris. You'd be a fool to play anything but Chuck Norris. 2) Would only be broken if playing Chuck Norris (or only Chuck Norris) wasn't an option for all players.
No, #2 gets broken because only the first person to draw Chuck Norris is able to influence the game - breaking the rule that everyone has equal opportunity to play. The other player loses all access to the gameplay. Additionally, because Chuck Norris breaks #1 and trivializes the game, even for the player who can influence the game the game is rendered unfun. His actual access to a game is also minimized. The situation is therefore bad for everyone.
Since this is MtG, this could be broken by turning it into a super-ultra-mega-rare card, or simply just selling it 1 million dollars per card. Only players with a sufficient budget would be able to play the optimal deck, i.e. nothing but Chuck Norris.
This still doesn't work. Whenever evaluating whether or not something is balanced, it pays to ask yourself the question, "Is this the sort of thing that is going to cause players to decry the situation or mechanic or game as 'unfair'?" The more reasonable the claim that the mechanic is unfair, the more likely it is that it is unfair because it is unbalanced. Remember, the whole point of balance is to provide weakness and advantage that can be situationally exploited so that there is a lot of interplay between players and between a player and the game mechanics. Even if Chuck Norris is a rare card for all players, he's still unbalanced. The notion that the game could be balanced by making powerful cards rare was destroyed by the very first MtG national tournament, where multiple players managed to put together "Chuck Norris" decks that always won on the first play - rendering the coin flip of who went first the entire game. But even as a rare win button that might or might not show up in a particular game, "Chuck Norris" is still not balanced.
Your RuneQuest example is an attempt to make a mechanic that is unbalanced, balanced - by resetting the game often. I've mentioned this before, and there are lots and lots of variations on it. One of the better attempts is to make a 'Troup' style game where players take turns being in the more important roles. Eventually, each person gets a chance to have spotlight, even though in any particular session, the whole session might be focused laser like on someone else. RuneQuest and early editions of D&D try to force players to play unusual heroes with unexpected, non-stereotypical abilities through randomization. I think balance is being deprioritized compared to naturalism, novelty, and other valued aspects of gameplay.
In my experience, it doesn't really work, or to the extent that it works it only works for a very narrow sort of playing style. First of all, there is no guarantee that in fact players will actually play several hundred characters. In fact, I'd guess in most cases that this doesn't happen. For one reason or the other the game is not actually reset as often as would be needed to ensure balance. This is either because people don't continue playing that long, or else because character rates of turnover end up being not that high. The result is in practice that you can have wide disparity between players in ability to share the game that ends up requiring some sort of ad hoc solutions by the GM or else a group of players that are ok with playing second fiddle, sidekicks, comic relief, and non-protagonized roles and who won't actually compete for spotlight. In the long run though, I find even this tends to break down. You tend to have players who willingly take those secondary roles in a story on the expectation that at game reset, they'll end up with a different perhaps larger role. But this is gambler's fallacy. In fact, there is a high expectation that someone who was unlucky the first time will be unlucky the second, third, and fourth time and it won't all actually come out in the wash. Someone at the table will tend to have the better sort of characters and someone at the table will tend to have the weaker sorts of characters. Eventually this will strain the patience of even the most accepting easy going RPer. Beyond that, there is an issue that once the novelty of these sorts of games wears off, players tend to acquire preferences about the sort of character that they wish they were playing and the fact that the game is actively thwarting their desires tends to create problems. Eventually, you find the players trying to work around the limitations of the game, either honestly by proposing rule changes, or dishonestly by simply cheating to get the character they want.
MtG is an interesting case, since card rarity is actually used as a balancing mechanism. I.e. type 1) balance could actually be achieved by breaking type 2) balance.
No, it isn't. Or at least, it hasn't been since the days of Alpha/Beta. Rarity is used as marketing device, to give impetus to players to buy more cards than they otherwise would want or need. But the assumption since basically the first one or two years the game was in existence is that rarity itself cannot be used to balance cards, and that in constructed all players playing at a high level will have access to all available cards. Even in draft, there has been a lot of design effort in every set over the last 15 years or so to ensure that there is reasonably good balance between rares so that draft formats are reasonably balanced and depend on skill and not just lucky draws. Compare a modern list of rares to something like the list of rares in Revised era sets, where often cards were slotted into rare if they had highly narrow utility. You'd almost never see that in a modern set.