By "balanced" I mean "every character design choice bring equal". It's a theme I've seen crop up both in discussion of things like D&D and in feedback on my own game design.
I think you definition obscures the point.
By "balanced" I mean, "produces generally functional gameplay so that there are no trivial strategies and there are roughly equal opportunities for all participants to win". This definition encompasses all games, and not merely RPGs.
So, for example, "Tic Tac Toe" fails this test hard. The gameplay is not functional, since there are a small set of trivial strategies that reduce the game to rote mechanical responses. The gameplay highly favors the person who goes first, as they have a larger number of effective options and the person going second is basically forced to only respond. Finally, in the end, neither player has a reasonable opportunity to win resulting in tedium.
In the context of RPGs, a game is not balanced if:
1) There exists extreme degrees of system mastery so that those with system mastery and knowledge of esoteric rules and combinations can produce characters that are much more powerful than those designed in a straightforward manner. A 'win' for an RPG implies everyone has fun, and thus the sort of design that promotes ever increasing system mastery which might be desirable in a competitive game, is not desirable in an RPG. That is not to say that no system mastery can exist, but that it can only produce a range of abilities that doesn't depart significantly from expectations. At a fundamental level, a social RPG is not a competitive game and you certainly don't 'win' by beating the other players, especially the other players of PCs.
2) The game produces such a wide range of potential power levels, that GMs and designers are unable to plan for the likely abilities that the characters may have. This is not to say that characters can't be more or less suited for potential challenges, or that they may have differing levels of ability. Players have a right to produce suboptimal and esoteric characters if they desire. What it shouldn't mean is that it is actually less straightforward to produce a suboptimal and esoteric character than it would be to produce a very useful and functional one, and even suboptimal and esoteric characters will have real strengths. It means that straightforward obvious choices shouldn't lead to suboptimal characters, and that this is discovered only through play. If this is not true, then a GM or designer requires very intimate knowledge of PC abilities and must tailor everything to the PCs. This is an advanced skill, tends to promote railroading (the GM is choosing whether or not the players succeed at all times), consequently tends to promote a high degree of illusionism, and obviously means that the game designers cannot write generic scenarios for consumption by the player base (which is almost entirely lethal to a game in the long run).
3) If it is easy to create characters that have no chance of participating. By default, though every character need not be equally useful in every situation, every character should be at least minimally useful in the games core concept of play. It should require significant effort and obviously weird and unusual choices to produce a character that can't contribute in the games core gameplay. For example, the core game play in D&D tends to be, "Kick the door down, kill the Orc, and take his Pie." Every character not intentionally made to be suboptimal in that core gameplay should be able to contribute effectively at every level of play. It should be hard to create an character that is not effective in combat, and there should be no traps where a character starts out reasonably effective in core gameplay but eventually becomes useless. On the other hand, if it isn't possible to design your character to be skilled in esoteric situations, then a game lacks the flexibility to encompass gameplay outside of its core focus. That also tends to be bad for an RPG in a long run, as it leads to tedious repetition.
4) Anything that absolutely or effectively breaks the core rule of RPGs - "Thou shalt not be good at everything" - is right out and must be excluded from the design. If it is possible to create characters that can resolve all challenges without depending on their peers, then that sort of character must be excluded as something that can be created because it renders the game non-social and ultimately non-interactive for every other player. If it is possible to create a character that can breeze through the sort of challenges a character of that degree of experience is expected to face, that character has to be excluded from those available to the players because it trivializes the game and renders it effectively non-interactive. If it is possibly to design a 'Johnny One-Trick', with a trick so strong, that every problem is turned into a nail that can be hit by your extremely effective hammer, that character has to be excluded from those available to the players because it trivializes the game and renders it effectively non-interactive. If the players of your game are speaking of "optimization" in terms of creating characters of that sort, you've created a defective game. Optimization ought to only refer to being able to accomplish what the player wants to accomplish through character design reasonably well, and the game is well designed when this is intuitive and requires no special knowledge. Regardless of how challenging game play is intended to be, CharGen should not be difficult. If 'optimization' is coded language for breaking the game, and you've got a percentage of your customers that are proud of their ability to do so and snear at those that can't or don't, you've already lost.
5) Your system should be designed so that to create an archetypal character requires straightforward predictable choices. If the best way to create a spell-users is to not create a spell-user, or the best way to create a brutally effective melee combatant is to not create a melee combatant, you've got big problems. For example, certain instances of the 'Elder Scroll' series had the problem that if you wanted to be good at something in the long run, the best short term strategy was to choose not to be good at it. Likewise, arguably the best way to build a 'fighter' in 3e was to play a different class as wizard or cleric optimized for melee combat was superior by RAW. Those are examples of extremely poor balance in your system.
In simple terms, your RPG is balanced if it is easy for a group of players with different experience level to create a character using any of the straightforward archetypes the game presents in such a way that in an average session each player gets a chance to contribute to the groups success, and over the course of the campaign each players contribution toward the parties success has been roughly equal.
Conversely, your system is probably over balanced if the only way to succeed in it is to conform very highly to the systems expectations regarding character builds and party composition. If there is no flexibility to approach tasks in different ways, your balance is impinging on player freedom too highly.
