Default-muted tags from admin-only tag groups are still visible in the user profile, muted tags setting

I created a tag named “muted” and added it to a group “admin-only-tags”.

I configured the group to be visible by admins only:

Next, I added the “muted” tag to the “default tags muted” setting. All good, all works as expect - the tags mute the topics to which they are attached.

However, non-admin users can see the “muted” tag in their profile, under the “Muted Tags” setting.

Is this by design?
I was under impression that “admin-only” tags would be such that I can freely add them to user profiles AND make it impossible for the users to remove them. I’d like the users not even know that those tags exist.