>If we presume that you could wave a wand and change the DNA using CRISPR all at once

If you wanted to just swap out one cell's genome for another, you could just physically remove and replace the nucleus, which has been used to clone mammalian cells. It's usually done with an oocyte and somatic nucleus from the same species, but it is apparently possible to create a viable embryo with a fusion of cellular material from two closely-related species, as was done with domesticated cows and Bos gaurus. (Linked paper is referenced here on Wikipedia)

While I obviously can't say for sure without empirical evidence, I'm quite confident that the mouse oocyte proteome is different enough from a human one that gene transcription would not be properly induced to create a human stem cell.

Finally, chromosomal structure and epigenetic modifications haven't been mentioned here. CRISPR/Cas9 gene editing doesn't provide the tools to restructure chromosomes, either in terms of the grouping of DNA into chromosomes or the packing of DNA into chromatin, nor does any other technology I'm aware of. I'm sure some researchers have been able to induce particular chromatin modifications, but much of how epigenetic regulation works remains unknown.