First, some enterprising fraudster will call/mail that they've acquired the loan and demand payment. Given how often loans are sold, it wouldn't take much conning to convince retirees that a payment is due and a check needs to be mailed to some P.O. Box.
Second, these companies that buy up loans don't seem all that technically capable. I fear that, one day, my parents' loan will be bought by one without an automatic monthly payment system. Again, someone with shady morals could start a company that looks to buy mortgages on properties where the mortgage is a fraction of the cost of the home and then not offer a auto-pay feature. When people inevitably miss a couple of manual payments, they could aggressively try to foreclose.
Both of these opportunities for abuse are made possible by banks with mostly positive reputations doing something that shouldn't be allowed. If a bank wants to offload debt that they've initiated, we should require them to continue to process customer payments on that debt and forward the money to whomever they sold to. Consumers should have the right to choose which companies they have business relationships with and we shouldn't have that relationship changed without our permission.