So, under your premise that the game system is about amassing power (no argument here), a character's ability to (let's go with bardic performance but it could be painting a portrait, whittling a sculpture, making a sword, etc.) sing a ballad is irrelevant in the world of D&D, if I don't misunderstand.
There are different definitions of "relevant" being used in this topic:
1. Relevant to the story at hand. A character that wants to play a musical instrument is relevant in this way precisely as much as playing a musical instrument arises in the story. There are any number of ways for the players to express this relevance, and not all of them are mechanical.
2. Mechanically relevant to the challenge of gaining power for your character, in ways that could be balanced via opportunity costs through some other ability you didn't take instead. A character that plays a musical instrument--
even in ways that matter in the story--does not necessarily qualify here. The assumption that the distinction does not matter fuels a lot of the "if you want to play miniatures" talk.
3. Mechanically relevant in some other way--exploration, simulation, aid to characterization, background warm and fuzzys, etc. 4E as currently written is pretty light on these. I think "backgrounds" might be the only place they show up at all, and the mechanic footprint there is very light. This gets back to, "if you want to make it matter, then really make it matter" talk that some of us have been saying. If this one bothers you immensely, then there is a good chance that D&D, of any version, is not your optimum game.
The way to get #3 is to quit trying to tack something onto #2, and thinking that it works because it is called "Perform" or "Feat of Flute Playing" or whatever. That is, either fish or cut bait.
Alternately, you can decide to expand the rules space of #2 such that these kind of things are mechanically meaningful to gain power. There has been some talk of that, too. But again, if you go this route, then the things you add have to be mechanically meaningful--at least if you want to be coherent. This mean, necessarily, somewhat of a change to the default assumptions about what "crafting" or "perform" really mean.
Trying to mix those three categories is a sign that someone hasn't thought this through, or that they don't really care about the mechanics but want their warm and fuzzies from pseudo mechanical heft--that is, having an entry on the sheet, any entry, is suitable to give them that warm feeling. To them, I say, what you want is to expand the Background option to have more choices, perhaps of narrower scope. Make a list, add it as a house rule, and you'll be happy! I'm sure WotC could do this for you, and make you even happier, but it won't take more than an hour or two to make such a list, and you can always change it later if you find something missing.
OTOH, if someone thinks that their warm and fuzzies not being satisified here is a sign of their (superior?) roleplaying chops, I suggest cultivating a wider RPG experience.
Edit: Somewhat ninja'd by Draco