I have asked this in the past but I had less knowledge of wikitree than I do today.
People's concerns about DNA privacy almost entirely center around autosomal, and significantly less about yDNA.
Two of the comments on another thread made by Peter Roberts caught my attention.
1. "Also, some auDNA testers have their profile as private. However on their immediate ancestor's profiles"
2. "If the ID was only on their [private] profile then there would be no useful information."
I believe that when we set a profile to private, we provide a name and way to contact the profile manager. But the useful information that we actually provide is enough
"for cousins trying to determine the shared ancestry of their [private and public profile] DNA matches"
I was asked to demonstrate the problem. I was give a profile and on that profile was a DNA match to a private profile.
Within seconds, I was able to know the parents of this person whose profile was private. I would not have been able to do this, at least so easily, if wikitree provided the same level of Privacy as yDNA and mtDNA. I would also not have been able to determine the identity of a private profile using yDNA or mtDNA so easily, if at all if yDNA and mtDNA used the privacy associated with auDNA.
I understand that implementing privacy is not perfectly secure, but that does not explain why yDNA and mtDNA are more secure than auDNA. It seems that people's concerns are the opposite as well.
Now, because the gedmatch ids are also provided, I was able to determine the mother and child were biologically related. I was also able to obtain an email address I might not have otherwise been able to get.
Edit: This is how you get the "immediate ancestor" of a profile, and how you get useful information from a private profile.