If you did make the interest rate attractive enough to get folks whose job is shopping for the best interest rate, you’re in for serious bad news any time the bank falls behind competitively risked interest rates. It will see massive outflow of deposits, be unable to pay them, and have to liquidate its mortgages, potentially at a severe discount (they’re illiquid by nature, right, and may have declined in fundamental value due to e.g. interest rate changes in the interim).
Now your bank is failing and, as soon as you do the responsible think and report insolvency or inability to satisfy withdraws, instant bank run.