I mean,think about it.
Ganon can use the triforce of power to do a lot of badass stuff.
Same for Zelda,she can use her triforce of wisdom to use magic!
And Link?His triforce of courage turns him into a frickin wolf from time to time ._.
SS Link did not just earn the Triforce, like WW Ganondorf or LttP Link. He became worthy of it. He was the only person known in Hyrule history to actually forge his soul to become worthy of all parts of the Triforce. So, when he collected it, he became its owner, and could wish on it freely.
A more simple way to explain Ganondorf's need to touch it is that there were multiple people who had a part of the Triforce, so the once who got the wish was decided by who touched it first. In this case, it is King Daphnes Nohansen Hyrule, former bearer of (most of) the Triforce of Wisdom.
It is possible that Malon's mother is a Gerudo or has Gerudo ancestry as Malon has vibrant red hair and her father, Talon, gives an interesting reaction when Link approaches him while wearing the Gerudo Mask, he will say that it looks like his wife, but then decides against it. If that is the case, that would raise the question on why she wasn't raised as a Gerudo (although this may be because of her differences compared to the other Gerudos).
i'd guess the triforce can choose what it grants but ganadorf's touch is powerful enoguth to override this.
Also, maybe the spirit of the Triforce of Courage (I.e Link) is above the rules or something.