I think you are misrepresenting the reasons people might object. From Wikipedia I gather 4 main reasons

https://en.wikipedia.org/wiki/Crazy_Horse_Memorial#Controver...

(1)

> Crazy Horse resisted being photographed and was deliberately buried where his grave would not be found. Ziolkowski envisioned the monument as a metaphoric tribute to the spirit of Crazy Horse and Native Americans. He reportedly said, "My lands are where my dead lie buried." His extended hand on the monument is to symbolize that statement.[18]

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(2)

> Elaine Quiver, a descendant of one of Crazy Horse's aunts,[24] said in 2003 that the elder Standing Bear should not have independently petitioned Ziolkowski to create the memorial, because Lakota culture dictates consensus from family members for such a decision, which was not obtained before the first rock was dynamited in 1948.[25] She said:

> > They don't respect our culture because we didn't give permission for someone to carve the sacred Black Hills where our burial grounds are. They were there for us to enjoy and they were there for us to pray. But it wasn't meant to be carved into images, which is very wrong for all of us. The more I think about it, the more it's a desecration of our Indian culture. Not just Crazy Horse, but all of us.[25]

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(3)

> Seth Big Crow, whose great-grandmother was an aunt of Crazy Horse's, said he wondered about the millions of dollars which the Ziolkowski family had collected from the visitor center and shops associated with the memorial, and "the amount of money being generated by his ancestor's name". He said:

> > Or did it give them free hand to try to take over the name and make money off it as long as they're alive and we're alive? When you start making money rather than to try to complete the project, that's when, to me, it's going off in the wrong direction.[25]

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(4)

> Other traditional Lakota oppose the memorial. In his 1972 autobiography, John Fire Lame Deer, a Lakota medicine man, said: "The whole idea of making a beautiful wild mountain into a statue of him is a pollution of the landscape. It is against the spirit of Crazy Horse."[26] In a 2001 interview, Lakota activist Russell Means said: "Imagine going to the holy land in Israel, whether you're a Christian or a Jew or a Muslim, and start carving up the mountain of Zion. It's an insult to our entire being. It's bad enough getting four white faces carved in up there, the shrine of hypocrisy."[27]

In his 2019 New Yorker article, ‘Who Speaks for Crazy Horse?’, author Brooke Jarvis states: “On Pine Ridge and in Rapid City, I heard a number of Lakota say that the memorial has become a tribute not to Crazy Horse but to Ziolkowski and his family”.[28]

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First, he deliberately sought to not have a place of honor for himself. Building one is incredibly disrespectful.

Second, his family wasn't consulted. That was too disrespectful.

Third, the builder is making bank on indigenous history.

Fourth, and crucially, this is a complete pollution of the landscape done essentially for vanity. This is maddening.

Note that those four reasons have absolutely nothing to do with any other Native American statue ever. Though I would agree that the representation of Native Americans done by non-native Americans can often be disrespectful (for specific reasons and not because it's a problem in itself)