The remarks you had about combat powers typically costing more than, say, diplomatic powers because combat tends to be more common is based on an idea of keeping characters balanced: They should get similar benefits from similar expenditure of points (or whatever you use to gain powers).
But balance is really an illusion: As you say, it depends on how often you get to use a power and how important that use is to the goals of the group (or individual). But that depends heavily on what these goals are and what opposition (active or passive) there are against achieving them. There is no a priori way to assign value to powers in this light.
There are, basically, two solutions to this. Both allow players to make the character they want with no regard to cost (though with GM approval), but differ in how the game is played later.
One approach is to require the GM to set up challenges so all players can use their powers to attain the goals with roughly equal importance (over time). So if one player designs a character that can lift mountains and the other makes a character with no powers except the ability to understand and speak all languages, the GM should make sure that the scenario calls both for lifting or smashing things and for deciphering obscure languages.
Another approach is to give the players a number of action tokens (or whatever you want to call them). Whenever a player wants to affect the story, she spends a number of action tokens proportional to how much they impact the story. Once a player runs out of tokens, either the player or the GM must find some excuse that makes the character unable to significantly affect the story until more tokens are earned: The character is suddenly called away on another mission, she gets seriously hurt and must recuperate, he is teleported to a faraway place, she temporarily loses her powers, or whatever you can think of.
Well, you're right to an extent, but I wouldn't say there's absolutely no a priori way to assign value.
For one, demanding things of the GM, or the group as a whole, is completely legitimate. If you design a game and tell the GM that he should run mostly combat scenes, then you can know a priori that there are many combat scenes in the game. If the GM chooses to disregard that request then he is, for all intents and purposes, ignoring some of the rules of the game.
It can also be infleunced with flavour (if there's almost notihng you can achieve with violence in the game world, then you can expect to have few scenes where violence is used).
Stricter mechanical means can also be used, if so desired.
True, to be able to know stuff about the game in advance you'd need to limit the possibilities and make the game more focused. But then again, I'm not a big fan of generic systems.
All this is not to say that your approaches are bad - on the contrary, they're awesome suggestions and can absolutely work. But what I'm saying is, you can do it the 'standard' way as well.