As the current behavior, there is only one option to update the accounting date to the First day of next open period.

While for the real business scenario, the user need the system to provide an option or a parameter to allow posting the approved expense report on the date when the expense report approval workflow is completed (expense report is finally approved)?

This is a practical issue as expenses will always be submitted after the month end. For example, it is logical to download the July expense statement from the credit card provider only after July is already over (to ensure that all the transactions for the month are included) and then import those transactions in the system.
The company need more time to approve this expense reports, and using the final date as the accounting date is the first option for some business.