private files area is available to all authenticated users by default. If your need is disallow all your users from accessing their private files area, you may also want to disable the Private files repository and the My private file block as well.
To disable Private files repository:
Site administration -> Plugins -> Repositories -> Manage repositories, then disable "Private files" repository
To disable My private file block:
Site administration -> Plugins -> Blocks -> Manage blocks, then click on the eye icon to to disable "My private files"