Whose Line Is It Anyway isn't a game. It's the name of an improv comedy show.
A
game show. The same format is also commonly used by comedy clubs and theater groups. There are plenty of other similar games that revolve around making stuff up surrounding preset prompts of some sort.
House, I've no idea about.
I'm referring to "playing house"; i.e. the archetypical game that young children engage in where they pretend to be adults and go through (frequently banal) daily activities.
Sim City is a solo game - and it's balanced the way solo games are, meaning that there is no one dominant strategy.
There are clearly some strategies that are better than others. There's also no real defined victory IIRC; it's simply a question of building whatever you like.
The reason I picked those three is those are all types of games that exist well outside of the D&D world, yet have a lot more in common with D&D than strategy games or wargames. D&D is improvisational theater, it is open-ended exploration of a character, and it is a world simulator. There are many noncompetitive games that share a lot in common with D&D, and few if any of them have any conceit of any type of balance. The Sims. Charades. The list goes on and on.
Of course, many competitive games also aren't balanced between participants/competitors. Take
Mafia for example; several defined (and totally unequal) roles create an engaging dynamic.
And even games that do have a concept of competitive balance don't
force participants to be equal; they just provide equal opportunity. For example, if I'm dominating the Scrabble scene by getting a Q on a triple word score every time, it doesn't mean that the letter Q is overpowered, it means that I understand the rules better (or have memorized more words that start with Q), which is how you win in Scrabble. If Usain Bolt keeps winning races, that doesn't mean the races are unbalanced, it means he's faster than everyone else. System mastery in D&D (say, picking out optimized Polymorph forms) is essentially similar to skill training for competitive games.
In terms of overall usefulness yes I believe they ought to be.
What about good ol' basketweaving? Is that supposed to be on the same level as using a sword? Trying to balance apples and oranges is doomed to fail. Even adopting a very limited, restrictive, dungeon-based setting still opens D&D up to a variety of capacities that will never be balanced with each other. A point in performance can't really be compared with a point in a saving throw to the level of rigor that would be required to enforce that level of balance. Likewise, a druid can't really be compared with a rogue to that degree.
"...If magic is unrestrained in the campaign, D & D quickly degenerates into a weird wizard show where players get bored quickly, or the referee is forced to change the game into a new framework which will accommodate what he has created by way of player-characters. It is the opinion of this writer that the most desirable game is one in which the various character types are able to compete with each other as relative equals."
Gary Gygax, The Strategic Review
So...if magic is restrained, everything's fine right? I mean, no one anywhere is arguing for unrestrained magic (which to me, sounds synonymous with at-will spells, so maybe someone is).
You confuse balance with symmetry. 4E is
asymmetric. Like e.g.
Fox and Geese. Or any wargame I can think of. Or any fighting game. 4e is balanced between PCs like a fighting game. (Who's stronger? Any good fighting game will have a lot of viable fighters) and between PCs and NPCs like Fox and Geese. These are both forms of balance.
What you're referring to as asymmetry however, while it may be a perfectly good model for wargames, is not appropriate for a roleplaying game. A roleplaying game is about the characters, not the players, and should be judged in terms of the characters' world and not the players' experience. The players certainly aren't competing with each other (unlike with a wargame), so as [MENTION=1932]Savage Wombat[/MENTION] notes, balance between them is irrelevant.