Your procedure seems very cumbersome. Who closes the loop on invoices being satisfied? Who monitors outstanding invoices, beyond due date? The bank has no information on what was invoiced, only that a payment was received.
How do you get reports on your expenses? Who reconciles your bank statements?
The procedure may work for you, but it seems very cumbersome with lack of control. If it works for you, great. I know it would not work for me.