I don't personally want to use a debit card for my everyday purchases, mostly for security reasons. I figure if I only use a credit card, then if the card gets compromised I can argue with my bank over the charges rather than asking them to put money back in my checking account while the fraud is investigated. Cashback on purchases is just icing on the cake.
Some banks go above and beyond for Debit Cards but check with your bank.
To any bank out there: I think if you offered a debit card that is backed by "virtual money" rather than the cardholders physical account, you would get my business in a heartbeat. The primary difference between the OP's answer is when your debit card is compromised, you are on the hook until the investigations are completed and still it is not a guarantee your funds are recovered.
set up autopay to pay the full statement balance each month from your checking account, so you don't have the hassle of dealing with it every month. then have all other monthly bills autopaid with your credit card(s), so you get points for that too. (this is what i do.)
you could also setup autopay against your checking account. in theory, it shouldn't be any harder to ensure you don't overdraft one time at the end of the month if you are already making sure you don't overdraft for each purchase, but everyone has their own weird hangups, so I'm not judging.
Re security: We allow you to have full control over the card for enhanced security: Ex: You can set daily spending limits, turn ATM withdraws on/off, and get instant notifications every time your card is swiped.
rewards that are comparable to those of a credit card
With a credit card, my rewards are a partial kickback of the fees charged to the merchant. Those aren't present in a debit transaction, which may have just a small per-transaction fee that doesn't vary with purchase amount.
Where does that money come from? Is the plan based on selling demographic or purchase history data to third parties?