I have never seen anyone claim this. Nor even close to it. And I frequent the Skull Kid support thread, which has some... optimistic people to put it nicely.
Skull Kid had a small dedicated fanbase that exploded after the LoZ stuff. Everyone sees it that way. Zelda one offs have consistently seen large amounts of support and then fall offs when they don't make it in, moving onto a new Zelda character next Smash. Want to know why? My best guess is because every Smash game Zelda fans jump to the next most recent character to support because they feel that that's the best chance they have. You saw it with Midna in Brawl and in Smash 4 Ghirahim had some support running for him before he was deconfirmed.
Skull Kid does have things going in his favor, but I think even the most diehard, blinded by love for the character fan can admit LoZ is what made them blow up in the Smash community. What you'll see them argue most of the time is that MM is an iconic game/object that is incredibly popular sure, but that doesn't translate into Smash character support and most people realize that. I'd imagine most people would be fine with him in but don't outright support him.
I agree with the general sentiment of your post btw, I just feel like Skull Kid is a bad choice to represent what you're saying when you already have people turning on him and saying he's gone most likely.
I agree with the sentiment of your post, particularly on how Zelda fans seem to jump from character to character. Though on Midna, Toon Link also had a lot of support, particularly so in Japan (Phantom Hourglass was the last Zelda game to sell over a million copies in Japan until Breath of the Wild's release). In general, there were various notably sized Zelda character fanbases during the pre-Brawl period (Midna, Toon Link, Tingle, and Vaati).
After Brawl's release, there was basically no strong Zelda newcomer choice for years until Skyward Sword's release. Even with Breath of the Wild's release (the highest selling game in the series), is there a particular character from that game people have gravitated towards?
The problem with the Zelda series is that there are only three major re-occurring characters in it (Link, Zelda, and Ganon/dorf). Impa might be the next most re-occurring character, but most of the time she is just an old woman (with the exceptions of Ocarina of Time, Skyward Sword, and the spinoff Hyrule Warriors). I actually think Impa would be a fantastic choice for an echo fighter of Sheik.
However, I understand the frustration of Zelda fans seeing as the series has now gone over ten years without a newcomer (and 17 years without a newcomer that is not a derivative of Link). However, aside from characters, the Zelda franchise is very blessed in content. It has more items based off of it than any other series in Smash Bros. with the exception of Mario. It also has the second highest amount of stages in Ultimate (nine stages), which is more than even Pokemon, and the only series it has less than is Mario (which traditionally even from the first game in the series, has always had significantly more stages than other franchises represented in the game).
I do think Skull Kid is certainly a contender for a DLC character so long as he is not an Assist Trophy or a boss. I think him and Impa are probably the only plausible contenders for a Zelda newcomer right now.
Perhaps a better example would have been Ashley.
