There's nothing stopping anyone from creating such a bank, but in economic times with high interest no one would put their money into a bank that doesn't pay in

There's nothing stopping anyone from creating such a bank, but in economic times with high interest no one would put their money into a bank that doesn't pay interest as they would have no hope of keeping pace with inflation. Also, if every bank operated in this way then no one would be able to get a loan and debt drives the modern economic systems. Meaning no one would be able to make investments based on debt anymore, at least not with a loan from a bank.