The Purchasing user guide suggests, "The Close for Invoicing status does not prevent you from matching an invoice to a purchase order or to a receipt." In that case, can someone throw light on what could be the purpose of having the status "Closed for invoicing"?
Other than reporting and information to the user who is looking at the PO Summary screen, I cannot think of any other purpose. Infact I have always used quantities in the po_line_locations_all to identify where this PO is.
I think accrual rebuild also uses the quantities, but I am sure somewhere they must have used these statuses to identify the accrual balance status.