You can resolve this if you create a Standard Group that has Access Level set to "Full Access", Privilege Set to "Custom" and just don't grant any additional privileges and give the site admin access to this group. Without granting any actual permissions they see Full JSS as an option at the top and when they select it they get access denied message, but they still have full functionality within the sites they are admins for.
One common variation of this is to make a Full Access group that has "Audit" privileges so Site admins can see the global settings and policies applied to their site, which also resolves this problem of not being able to do things within their sites.
