This is certainly the case for credit cards, and in my experience, with checking accounts. The bank or processor will manage the investigation and go after whomever stole the money to recover their loss after reimbursing you.
Interestingly, I had someone steal my debit card several years ago, and they went to CVS or Walgreens (can't quite remember). They purchased Visa gift cards, and had video of the transaction in which my card was used to purchase a Visa gift card, so they should be able to have Visa provide the information about the stolen card or at least void it, but they will not. For some reason, Visa et al have decided that it's better for them to just eat the several hundred dollar cost of the card.
It's probably the same kind of calculation as fix vs. buy new. If it costs you $50 to just buy a new one or $150 to hire a repairman, you'll just buy a new one.
Interestingly, I had someone steal my debit card several years ago, and they went to CVS or Walgreens (can't quite remember). They purchased Visa gift cards, and had video of the transaction in which my card was used to purchase a Visa gift card, so they should be able to have Visa provide the information about the stolen card or at least void it, but they will not. For some reason, Visa et al have decided that it's better for them to just eat the several hundred dollar cost of the card.