I haven't had this problem with my bank just pointing out the inherent differences. With a debit card you are relying on the cyber security and data retention policy of the store, the bank, and the electronic network provider.
Now I realize that if your account is used without authorization most banks refund the money. This can take a certain amount of time and could lock up your remaining funds in the meantime.
Less than a month ago my card details (the magnetic stripe) got swiped. However my bank noticed the funky payments, automatically detected the issues, temporarily froze the card. Then when I noticed it didn't work and called them they temporarily locked up the card for a single use, and then blocked it permanently and sent out a new card.
I noticed it on Thursday, I had the new card and all unwanted transactions rolled back on Monday.
This for a debit/Visa hybrid card, which acts as Visa out of country and on the Internet.
Also, the bank requires me to temporarily unlock the card for 'unsafe' Internet purchases before usage, which basically is all purchases that don't involve 2FA.
Now I realize that if your account is used without authorization most banks refund the money. This can take a certain amount of time and could lock up your remaining funds in the meantime.