I think inflation could hurt the banks. Inflation helps debtors because they pay back loans in less-valuable money. Conversely, it hurts creditors, because they are receiving less-valuable money.

Consider this; a bank is loaning money out to people to buy houses. The interest rates for these loans are fixed at 5%/year. What happens if inflation jumps up to 30%/year? The banks are taking a 25% hit.