You can mitigate by keeping two accounts. In your debit card account you keep a minimum balance and transfer funds in as needed to cover purchases. For automatic ACH payments (mortgage, etc.) have those come out of the other account that does not have a linked debit card.

So worst case you are without a small amount of money during any dispute/fraud resolution period, but your major regular ACH payments are not at risk.

The downside is having to monitor your balances closely and transfer funds more often (which can sometimes involve a fee but if you shop around you can find banks that don't change a fee for inter-account transfers).