Those "free rewards" are not free they are factor into the cost. Nothing is free. One way or another you pay for it.
if you are referring to the price of the item, then you pay the same price too....even if you pay with cash. So why not use a CC?
If you are referring to the price of the card -- then I don't see how. I don't pay interest on the CC, the only annual fee CC I ever had was my SW Visa that got my thousands of $$'s in free (sorry, $69 annual fee) flights.
We use a CC for everything -- unless it costs more to pay on line (i.e. school book fees/HOA dues) then we just write a check.
In addition to the free flights, I couldn't begin to calculate all the free hotels my no annual fee, never paid interest on Hilton Honors Amex card has gotten me....or Disney $'s from my no annual fee never paid interest on Disney Visa.
If you know how to maintain a budget, CC's are a great way to earn free rewards of your choice.