This is going to be a rather volcanic topic I reckon.
I'm going to say that the question feels loaded. In some systems, allowing any power to be rewritten to fit any concept/template/class - works fine. In others it can/will crate thematic problems. In others it can/will create game balance issues.
I'm going to preface my opinion with a disclaimer; then go to town on the topic.
People are going to do what they want at their table as they see fit. People are going to ignore our opinions and topics if they see fit. Many people who play this game likely do not even go to this forum. I see nothing wrong with house rules. I use them all the time.
Ok, now that I "covered my ass", we can get down to business.
I think allowing every character to have the justification to do what every other character can do, grants an incredible amount of freedom. That is very nice for some people. Freedom can be overwhelming though. With so many options; making those decisions on what to play and what to spend refresh on becomes ever so much harder. It can also make chracter cration and spending refresh take so much longer with so many options available.
Harder because some people like to be unique. The option of every power being just a tool and able to be remade to fit any build removes such unique-ness (um, yeah, that is a word now
) possibilities.
It also makes character roles in games sort of less important. I don't have to play the groups "fighter/tank". Anyone can do it as well as I can or better. While I suppose this can promote a player to buy things with more freedom, it can also create a feeling of not mattering.
The options freedom grants certainly makes for a vast number of playble options however. I suppose there is something to be said for that.
I think it can be a paradise for munchkins both benign and malginant. (See, I can make munchkins not seem all bad) I think the former sentence bears a lot of thought. The number of powers and stunts that can interact widens dramatically and could in theory damage a game (while making a player or players feel very badass).
Ultimately, some players need limits. My group has a player that does indeed need such limits and will gladly admit it. I have met too many people who ignore concept and template and simply buy powers and stunts that are the most efficient. I've even been tempted to do the same thing. My opinions on this matter remain colored by that.
I honestly think some powers should remain the domain of rare beings and or creatures (or only be in the hands of the GM even). I may be in the minority but, such is my opinion.
So I suppose I believe that certain powers regardless of retooling should be disallowed to certain concepts, based on the following:
First and foremost - game balance: The GM must
be able to challenge all players (unless the gameer group disagrees). Every player should feel like they matter to the story and if possible the action at hand. Some power combinations on some characters can hamper this.
Second - concept should be followed: I think this encourages roleplaying and makes the game feel more immrsive. (again, YMMV)
Third - limits can spark creativity as much as it can hamper it and some players straight up need limits (again YMMV)
I tried to be as concise and non confrontational as possible. I can't guarantee this will prevail all the time as this conversation will likely heat up. Hey I tried!