The appeal mainly comes from Fire Emblem Warriors which depicts her as a ninja-warrior who can channel Sheikah magic and has a no-nonsense personality.
Personally, I like Impa slightly more than Sheik because at least she's somewhat relevant in the games she appears in whereas Sheik has nothing going for her beyond a plot-twist that doesn't add much and a cool turban.
I'd argue that Sheik is much more prominent than Impa. Impa only makes three appearances in Ocarina of Time, and none of them that significant. First, she teaches you Zelda's Lullaby and escorts you out of Hyrule Castle. Second, she flees with Zelda from Ganondorf. Third, you go rescue her in the Shadow Temple and she becomes a sage. Based on that alone, she's not much more notable than, say, Saria. Like you said, the appeal mainly comes from Hyrule Warriors, but a lot of other characters are cool in that game, too.
Meanwhile, Sheik meets you regularly as an adult, telling you cool bits of wisdom and teaching you
Guns N' Roses songs. The twist doesn't add much to the plot (and it's laughably terrible when executed in Hyrule Warriors), it is notable for giving Zelda more of a role than damsel in distress... which she goes back to immediately after changing back from Sheik, so Nintendo tried to have their cake and eat it too, it seems. Same thing happened in Wind Waker, oddly enough. But the idea of Princess Zelda being able to take on this alter ego and become a wise ninja to help Link in his quest is one of the more unique elements to Ocarina of Time's story.
I think people are just more inclined to rally behind who they see as likely. Impa wasn't the most popular character, but the fact that she was recurring made her seem more likely in eyes of a lot of Smash Fans, since it dodges the "no one-off Zelda characters" fan rule. Likewise Skull Kid got a huge boost in support after Loz18 trolled the fanbase and Ghirahim was popular during Wii U speculation because of Skyward Sword's relevancy.
And just to be clear, I think Skull Kid and Ghirahim both had the potential to be great additions, and I'm not the kind of person to gatekeep people for "bandwagoning", so I'm not saying this judgingly. I'm just stating why I think the situation is the way it is.
Well, Impa is recurring, but the iteration of Ocarina of Time is an outlier. All other versions of Impa have her as an old woman, while OoT has her as a younger ninja, so the Impa that people are asking for has just one iteration (outside of Hyrule Warriors, where a lot of things were reiterated).
I also thought that it must be a "no one-off Zelda character" rule, but then I realized that many Fire Emblem characters on the roster are also one-off characters, so either that's not really a rule, or there's a double-standard going on. Several other characters are also "one-off" characters in the sense that they only appear in one game, so recurring characters doesn't seem to be that much of a limitation. To top it all off, Sheik also only appeared once, yet she's never gone anywhere. I think the issue is moreso that there's too many characters to choose from at this point, so narrowing down who is too daunting of a task.
If there'd been a steady pace of Zelda characters, we could've had Skull Kid, Midna, Ghirahim, and, maybe Mipha now or as a character in the next game. Throw Zant and Vaati into the pool, too. That'd be the same kind of pace Pokemon and Fire Emblem got. I'm really curious as to what the behind-the-scenes reason is for why there's no new Zelda character, since I'm sure it's going to be some weird reason none of us would ever guess.
