The big problem with debit cards is if you get it stolen then your money is taken. Sure you'd get it back eventually, but until them you don't have access to your own money and can't spend it.
That's weird. I live in a country where 95+% of all payments are done with debit cards, and I don't know anyone who ever had a problem with fraud.
Maybe debit cards are a bit better at security than "oh let's copy this number and put a fake signature on a piece of paper"? Even the mag-stripe version of our payment system that we have had here since '79 required online PIN verification.
You have awful fraud protection and zero to near-zero rewards.
Banks will give you net-30 terms for no cost, reward you with many benefits, and give you fantastic protection from thieves AND retailers.