That ninja part can also be covered by Impa. Age of Calamity Impa specifically. She could be based around Sheik's basic playstyle but with her own gimmicks and of course own moves. Kinda what would have happened if Lucas actually replaced Ness in Brawl, but to a further extreme.
Zelda has made up moves, sure. So does Sheik. Zelda can have a moveset by now using more of her source abilities. Sheik doesn't, or well, could if they take stuff from the first Hyrule Warriors and maybe the Yiga enemies of BotW / TotK.
Anyway I'd outrightly replace Sheik with Impa here.
No, it can't.
Because they are completely different characters. Impa has evolved into more than a Ninja and is a powerful caster and time traveler, as well as a very strong woman in some cases, and uses a completely different weapon while having no strict age when she can fight.
Sheik is solely a ninja. Impa is sometimes a ninja and can be tons of other things. She is best thrown in as a unique character who has niches that Sheik doesn't cover. We don't have a proper lance/spear-like user, for instance. We don't have a muscle woman either. We don't have a woman that even looks somewhat older(30+) playable. She covers stuff that Sheik can't. And Sheik still has zero good reasons to get cut either way. She's easy to make by now and provides a completely unique niche that is entirely different from Greninja. Replacements are pretty silly in the first place and undermines why people like the characters.
Here's the problem with Zelda trying to do BOTW stuff; it's a completely different character entirely who has a different personality and ability set. Just make another Zelda instead of trying to completely alienate the fanbase. There's nothing wrong with Zelda's main moveset, but she does need more tweaks so she's easier to work with. Sheik is just fine balance-wise, in comparison. Besides, who cares if it's made-up. More importantly, Zelda is directly a magical princess with grace and beauty. Changing that undermines her core function as a playable character, thus, making it a severe change. I mean, this isn't asking BOTW Zelda in her dress to be playable with mostly the same moves, but updates a bit with some Champion or other visual stuff to slightly change it to be possibly better. That made some sense because you are tweaking them, not making a blatantly new character.
If you are talking about making a new character, you are just cutting another one. BOTW Zelda, as talked about, is basically a new character in practice. She's not some floaty person. She obviously knows how to use magic, but it's done a lot differently too. She's not the same kind of barrier maiden. It's actually a lot easier to understand why Sakurai didn't go with her. They act super differently. She's not a graceful person in the same way. She's not really regal. She's a different kind of adventurer. Meanwhile Link has never changed much among the games bar being more emotive and sometimes being more silly or serious. It's why you can somewhat change it. Not even his change into Ultimate was more than a few tweaks. He's still odd to use(due to no Gale Boomerang), but it's not a severe change-up. Bowser and Pit were the most changed up anyway, and they still function mainly the same. The most, really, that felt odd, was Pit no longer being able to glide. He lost one core move(Mirror Shield) for the Orbitars, but mostly stayed the same. And as alienating as Bowser and Ganondorf are with their changes, they still function the core same way, for better or worse. That's the goal of moveset changes.
There's nothing wrong with wanting a moveset overhaul, but it makes sense why it's not done(we've had some fairly big ones, but never a straight-out different character). Characters also have never gotten truly replaced either. Not once. Toon Link wasn't a real replacement, but someone taking a similar role to Young Link due to a lack of time to have both in. They are semi-similar, but we already knew it wasn't a replacement the second Ultimate showed Young Link is a different character. ...Which he is, mind you. Maybe at the time, sure, but let's also note some factors of why; Toon Link had a similar moveset and while playing quite differently even then, had the same core role(a child Link). Both being there didn't make much sense. It's the latest child design. But he's still treated as someone else, being a cartoony overhaul based upon the Wind Waker model(and various toon-inspired games).
This is even the only time where we had something that can be called a legitimate replacement. I know people accused Lucario of that for Mewtwo(thematically, they have some similarities), and Ike for Roy(again, thematically they're partially fire swordsman with some heaviness to them, though Ike is way more heavy. They share few moves either way). Pra_Mai may have been Plusle & Minun, and that replacing Pichu does work since they use the same actual bodyshape(hell, they could've been an Echo in all but name, due to being two, if they wanted to in Ultimate. But that requires a looooooooot of work. They might've been a minor idea at best. With the A.I. being hard to program alone, you also have to figure out what should make them different. As they aren't like Ice Climbers, as both do have their own moves and even abilities. So it'd be closer to a Switch-out Character,, as in who is in front. But both would be there. I could go on, but them being scrapped, if it was them, was most likely due to how difficult the idea really is).
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Speaking of, nobody should get a moveset overhaul. Just update them. Tweaks are good. Ganondorf absolutely needs them(a lack of a reflector is his biggest hurdle, but also few good approach options). Alienating the fanbase is not worth it and these overhauls do nothing but help competitive players, the smallest set of the players. Turning casuals off from the game is a far bigger deal. Tier lists will always exist anyway, and somebody will take the bottom spot at some point. It shouldn't be the same character often(unless they're an actual joke character like Pichu and Jigglypuff were), since that just means there's a balance issue instead.