Sorry, but the current system is backwards. You are restricting admin access to their own site, which makes website management very tedious. I am not sure how something like this could have been overlooked in development.
The logical approach is to give admins full access. We can then use the preview bar to limit our access ONLY when needed.
Thank you for this suggestion! This feature request, or some aspect of the functionality suggested, is currently being reviewed for possible inclusion in a future update. If there is additional information, this post will be updated to reflect it.
My theme (Divi) doesn't allow me to access the "preview bar" making matters worse. Is there a way to change default access role for administrators?