Hi Steve,
you're right if you start from an empty task, but if you start selecting secondary admin task you can see and add all the "admin" tasks just appset and application isn't available because they are typical for Prim or System admin, but it also very strange to have a possibility to create or delete appset\application and don't have the possibility to define security.
Other possibility is to create a copy of prim admin profile and modify it through SQL the SecuTaskAccess table at your own risk.
Regards
Roberto