We too can use debit cards that way. The laws regarding fraud liability differ between debit and credit. As such, credit card providers generally have fraud detection departments working around the clock, whereas the onus is entirely on you to report fraudulent charges on a debit card within so many days of the charges appearing on your monthly statement.
OTOH there's the hidden cost of transactions, which the seller pays (and that's where the refunds come from), which admittedly won't go away if it's just you who stops using credit cards.