Game balance can be a controversial topic. Some feel it is paramount, while others feel it is just a tool among many.
I don't think it's really controversial in that sense. Everyone realizes on some level that a game needs to be at least somewhat fair, and that a game as complex as an RPG needs to be balanced. 'Realizes' in the sense that they'll notice they're not having much fun playing a game that's unfair (especially to them) or imbalanced (likewise). The controversy comes in because imbalance in a complex game can be leveraged by those who understand it. And, because designing a balanced game and retaining balance when modifying it is /hard/. If you're not up to the challenge, its very tempting to 'sacrifice balance' for some other quality (sometimes it's even the right call, examples below). If you're vested in imbalance, it can, similarly, be justified by a refusal to allow some other quality (real or imagined) to be 'sacrificed for balance.' You can even go on about a game being 'too balanced.'
And, people can buy into that. When you think about it, a game as complex as an RPG has a lot of qualities, a lot of elements that make it up, a lot of different approaches to enjoying it. For almost any gamer, there's probably some quality that seems more important than balance. So, if you're trying to justify imbalance (not prioritizing balance, say), you can pretty easily get a majority of players to agree that balance may be important, but there are 'other things' that are more important. As long as you don't give them a chance to try to hammer out a consensus of even slightly objective qualities that they can agree are more important than balance, because they're going to have a very wide range of priorities, indeed. Of course, there's always the resort to subjective qualities. Especially 'fun.' Everyone knows a game is about fun, and fun is a subjective experience, so we can all agree fun is more important than balance (or whatever other quality you don't want to put in the effort to design into your game, or need to sacrifice for something else). But it's meaningless, because 'fun' is a chimera, it's different for everyone, you can't design it in, no matter how much balance or how many other objective qualities you sacrifice at its altar.
Personally, I feel that these days folks seem to view balance as the end goal, while I feel it's just part of the toolset.
Balance is hardly the goal, it's just a very helpful quality that games can possess in varying degrees. You might even say that it's vital. Necessary for a good game, but not sufficient, in itself.
After all, a perfectly balanced game is this:
Everybody roll 1d6. Highest roll wins.
That's a very simple game. It's even a perfectly fair game. But it's not balanced at all. I suppose you could say it's not complex enough to have the quality of balance in the first place, let alone to have or lack it to a given degree...
...but, I've gotten way ahead of myself. First, we need a workable definition of 'balanced' to really make sense of it. One definition I came across that seems to work really well, for me, is this:
A game is better-balanced the more choices (in both relative and absolute terms) that are
both meaningful and viable that it offers players.
Your example offers no choices at all, so lacks balance, completely. It is, however, fair - each player has an equal chance of winning.
Now, a game can offer many viable & meaningful choices, and /also/ many more choices that are non-viable but meaningful (or otherwise attractive to players). The number of meaningful & viable choices in such a game is relatively low (relative to the number of non-viable choices). You'll hear people criticizing such games for having 'traps,' and you'll hear others describe such a system as 'rewarding system mastery.'
Imbalanced games can be fun, actually, especially complex ones. Especially fun for those who have mastered them, when playing with others who have not. They can also be fun (more or less by accident) for those who haven't mastered them, but who all end up making choices they find meaningful, that happen to be viable relative to the choices each of the others have made. Amusing, that. (Even weirder, an imbalanced game can yield a balanced meta-game among system masters, a sort of emergent balance, once all the traps and chaff have been eliminated from consideration.)
Better-balanced games, OTOH, can be fun for everyone playing them, masters or not.
How do you feel about balance?
Obviously I've thought a lot about it. Pardoxically, I find it very important, but not a goal or a be-all and end-all of design. It's just something you shouldn't screw up or sacrifice trying to accomplish your actual goals (unless your goal /is/ imbalance - imbalance does serve goals like rewarding system mastery, and can be leveraged to serve other, softer goals, as well). That is, if your goal is to create a good game. Being good in that technical sense isn't always an important goal.
A more important goal if your writing professionally is to appeal to an audience. There's really no telling what might do that, but, hey, if one imbalanced game is wildly successful (by the standards of the market for such complex games as RPGs, so that might not be saying much), then it's worth trying another that's imbalanced in similar ways. WotC, for instance, was very successful with M:tG, which featured, among other things, attractive-distractors, cards that looked cool or useful, but were really sub-par. "Timmeh cards." Traps. The presence of non-viable but at-least-seamingly-meaningful options deepened the system mastery element of play, creating a balanced, and challenging meta-game. It's hardly surprising that they designed 3.x along similar lines. (And, no, I didn't just make all that up, have to give Monte Cook credit for those insights - Ivory Tower Game Design, he goes into it in laying the foundation for his main point, but it's interesting in its own right.)
Rewarding system mastery may sound a little cynical, but it's not the only reason to design imbalance into a game intentionally. (Not just design, either, but modify - we DMs love modding D&D, and often, what we're doing is inserting imbalances, intentionally, with good reason.) If you want to influence player choices, one obvious way is to make some choices more attractive - either more meaningful or interesting (qualitatively) or 'cool' (highly subjective) or simply more effective (quantitatively). Take the game I started with and still love: 1e AD&D. It was the first RPG, and it was a medieval fantasy RPG. One of the classic archetypes is the knight in armor, another is the hero with a sword (not just any sword, the high-middle-ages cruciform swords we all saw in Ivanhoe - because 'we' here is contemporaries of Gygax and Arneson). The game doesn't just give you perfectly realistic choices or perfectly balanced choice and trust you to choose plate armor and a long sword because that's the image in the genre. It makes Plate 'Mail' the best armor in the game, and it weights the magic item tables to make longswords the most frequently-found (and most varied, and among the most powerful) magic weapons in the game. That's imbalanced, it's making choices like specializing in the Glaive-Guisearme into 'traps' - but serves a purpose, by narrowing the scope of play, without narrowing the sweep of the setting.