Admin permissions are required to set 'limit to' or 'also add' participant role for scheduled reminders?
Two explanations come to mind:


Scheduled reminders are often set up by administrators so in many
cases the current arrangement is fine. 
CiviCRM:Administer CiviCRM is a
default requirement so it is possible no-one has worked through what
permissions make sense if it is not an administrator configuring the
reminders.


I'd suggest you create an issue at https://lab.civicrm.org/dev/core/issues and describe how you think the permissions should work in that area.  

However, unless you can contribute code or sponsor someone to do the change, it is unlikely to be implemented quickly - but you might get lucky: sometimes people getting started with Civi development are looking for small changes to work on.