In my experience, this is only the case if you set up the payment through the bank's automatic payment system, which typically uses paper checks (but may do an electronic deposit for some payees who have specially registered).

Most subscription-based businesses that go to your bank account get an authorization to do an "ACH pull". In some instances, this authorization alone can act as collateral (e.g., in securing payday loans or medical payment agreements). As such, I would assume that allowing consumers to revoke the authorization is more problematic than it sounds.