How does using swords and magic make him not represent power? Power =/= punching and kicking. It's not like that is what makes him powerful. Does shiek represent power more than Ike? Because shiek uses punches and kicks and Ike only uses a sword. Ganondorf can be just as strong and use a frickin sword. This argument literally makes zero sense. And Ganondorf using the falcon punch does not make sense just because you can picture him doing it. I could see Link punching and kicking too. That doesn't mean a punching based movesets would be reasonable for him, and it certainly doesn't mean he should have that over his weapons. That's silly. So what if ganondorf has a punch or kick here and there in tp? Why does that mean his primary weapon, the one he actually uses when you fight him, should be taken away? That's like saying link should have a sumo wrestling based moveset because he did that in tp too.
Because power is about physical prowess, not magic alone. It doesn't "show power". Power is about being near untouchable(like with super armor), sending people flying. Power is basically Strength.
No, moves makes sense because one can picture them doing it. Otherwise most movesets wouldn't work. If it has to fix what the character can potentially do. Ganondorf himself has very few canon moves to draw from to make a full moveset, unlike, say, Mario, who has most moves covered. Even Link has to get a few unusual moves. Not to mention Zelda. And Sheik. And Peach. Etc.
Movesets absolutely need to be coherent and can't just be random canon moves. They need to flow right. This is something Ganondorf always did.
Also, what weapon? You mean the weapon he didn't pick up outside of WW, his own swords, and the Sword of Sages he stole from someone trying to execute him from it? He doesn't have an actual regular canon sword like Link does. Being a swordsman is just one of his many traits. Him overpowering others is a huge thing for his characterization, and having the de facto highest strength in a fighting game, which lets him overpower others, is a very strong representation of who he is.
Lastly, keep in mind the main Zelda trio(so not Sheik, really) heavily represent their Triforce pieces based more around what the series is. Link is Courage, able to handle any weapon and various tools. Zelda is Wisdom, and has always been a primary magic user. Ganondorf is Power, who does it in various ways, but mostly was able to push everybody around easily due to his immense strength, something shown way more with TP Beast Ganon(who, fyi, isn't a primary magic design, but a physical brute). Using a thin sword that is about finesse, not power strikes, wouldn't even work well. His only move is a simple stab with it in Smash. It's not a huge sword like the one in the GC Tech Demo, which fits Ganondorf better. His actual sword usage was never "power" so much as technique. He only used brute strength and some magical moves otherwise to show off his power. This isn't even counting Ganon in OOT, who is a boss that is mostly physically assaulting you, using hard-hitting swords. Ike is basically what Ganondorf needs to be akin to to represent Power as a Swordsman(not the same moveset, but more the same style of extremely strong strikes, something he does in Smash as a clone anyway). He doesn't actually use his Swords in any way to represent Power in the canon games. Only HW, which explicitly even uses Smash Bros. moves like Warlock Punch, further showing that magical brutish attacks are still a valid interpretation of him(never mind his Flame Choke is a canon move based upon stuff he did in WW and TP. He can and will physically assault others. He absolutely punches. The only real point to consider is that he's not much of a kicker, but to pretend he doesn't go punching around his enemies is completely wrong).