Isn't invoicing also a formal way of extending credit (or IOUs) to other businesses. It makes perfect sense in the situation where there is high trust between parties. However it sucks for the person extending the terms because they're out of pocket until payment is made (if at all it is made)
Accounts payables/receivables makes complete sense for larger companies -- they are established, there is trust built between the 2 parties, and it gives companies flexibility in managing their cash. But for micro businesses and professionals whose counterparties are new in 50% of cases, the big-business invoicing mentality actually creates more problems than it solves.