I work as a network admin for a small community bank, so I have a passing knowledge of these matters. First, fully investigate your rights under Reg E if you are in the US.
There are rules that govern reporting unauthorized transactions and the providing of "provisional credit" by the financial institution. Make sure you read and understand your rights. Hold your institution's feet to the fire, and make sure they act within this framework.
Second, understand that it is difficult to protect your debit card information. It can be stored (and stolen) from so many places. Any online purchase may result in your card info being stored on a server somewhere. Once that server's back end database is compromised, your data is exposed. Or you shop at a store with a POS system that is not well secured. Or your server at the restaurant last night cloned the mag stripe on the card. Ad infinitum.
Now, it's easy to say "make the financial institution liable for all fraud". But keep in mind the sheer volume of ACH payments processed by some of these banks. There's no way in hell that a bank can know for sure, 100%, that you did or did not initiate a particular transaction. However, please know that most banks' core providers have heuristic/behavioral analysis that does in fact look for behaviors that don't match yours. Companies like Fidelity National Information Services (FNIS), for example, actively send out "fraud alerts" that monitor ACH and debit activity on their networks. For example, if your card is used to purchase a product from a country or a domestic location that doesn't match your activity history, your bank can be alerted and the card can be "hot carded". I know it seems like we, as banks, drop the ball a lot, but keep in mind there is a lot going on that customers are not even aware of.
One piece of advice I would give is to just keep enough in the DDA account to which the card is tied to not go into an overdrawn status. Keep the bulk of your funds in a NOW or savings account with nothing electronic tied to it. No debit card, no automatic bill pay, etc.