I agree in part with your point.   I have been working hands-on in business and accounting, and closely with CPA's and corporate attorneys for 48 years.  Customers/clients must adhere to the agreed-upon payment terms outlined in the contract or invoice.  However, many businesses grant terms without a "contract".  They just state the terms on the invoices. If the customer has multiple outstanding invoices and pays some of them, businesses must apply those payments according to what the customer says they are paying.  In some limited cases, if a customer has multiple outstanding invoices and does not specify which one to apply a payment to, the business might apply it based on their own judgment, but this should be handled with transparency.  Additionally, when there is a dispute on an invoice and the customer short-pays, it is not prudent for the company to apply the partial payment to another invoice. 
Thank you for sharing your thoughts.  If you have further debates on this, perhaps we can chat separately.