WooCommerce only completes an order automatically when every item in it is both virtual and downloadable. Everything else waits in Processing until someone marks it Completed by hand, including event tickets, class registrations, memberships, services and bookings that never need to be shipped.
This plugin completes those orders for you. Set your rules under WooCommerce MCW Auto Complete Orders, grouped into Products, Fulfillment, Payments and General tabs. When a paid order reaches Processing and any rule matches, the order is marked Completed and a note on the order records which rule matched.
Order rules
Product rules (every item in the order must match)
Customer rules
Built for WooCommerce