Hi Scott,
Not sure if I have under stood your question correctly, but here's my immediate thoughts . . .
As you have rightly stated, users with 'collaborator' license type (reviewers and requesters) cannot change task statuses or edit tasks in general, as a result reviewers cannot initiate or create an approval process. They can however be assigned as an approver. A user with a work or plan license can initiate an approval process and assign a reviewer as an approver and dependant on how you configure the approval process, the task status will automatically update (with some limitations) based on the approval decision given by the reviewer (i.e. if rejected, change status back to 'In Progress' / if approved status will change from 'Complete: Pending Approval' to 'Complete').
Another thing that reviewers can do is request document approvals. I'm not sure what / how you are using approvals in your system, but if a document approval could be appropriate instead of a task approval, you could bypass the need to be changing statuses to initiate approval processes by using document approvals instead.
Best Regards,
Rich.