You're not participating in a good faith discussion. Yes, it is technically a line of credit but it's not the reason why you're being refused service. Overdraft risks for a personal account are small and can easily be accounted-for in the service fee or via insurance (which is the same in the end).

The reason for account closure is the fear of anti-AML laws and sanctions that have nothing to do with loans. Banks in fact love offering small loans and it's not uncommon to have your account closed while having a pre-approved loan at the same time — these are different bank divisions in action.

And in any case, turning personal debit accounts into credit accounts is not something that was asked for. I lived long enough to have used Visa Electron and Maestro cards that made most of overdraft scenarios impossible. It was the banking industry decision to get rid of them.