Why would a company insist that any customer who fails to pay an invoice when due must replace it with an interest-bearing note?

To negate his loss. To encourage payment in full and know that his "loan" to the buyer will never increase.

Suppliers who state interest charges after 30 days often find their bills paid without the interest, months late. Maybe this is an attempt to add a new legal emphasis to the interest.

When companies do not get paid when due, this affects their cash flow. If they do not have the cash to pay their bills, they could be losing money to borrow to pay their bills.

So a vendor that does not pay their invoices on time is costing the company money. Usually the invoice states terms that if the invoice is not paid by a certain date, interest charges accrue. So a promissory note is probably not necessary, but does give a company added leverage to collect on money owed.