There are a number of benefits to using credit cards that cash doesn't have:
1. Build a credit score
2. Fraud protection
3. Related to 2, but if I lose my card it's not a huge deal, cancel it and get a new one. If I lose 300$ cash, it's just gone.
4. Rewards! ( 1-3% back on 20K spending per year is a few hundred bucks )
5. Extended Warranties. Often times, you can get an extra year or more on warranties through your credit cards. That's why I put my new kitchen appliances on my Amex.
6. Free loans! I re-did my kitchen last year at about a 10K cost. Although I had the cash to do so, I instead signed up for a new card with 18 month 0% interest. That gave me another year and a half of saving before paying that off, so it's less of a hit to my balance at once. IMPORTANT I would not have done this if I did not have the cash to pay this off at any point in time.
It's really, really simple too - just pay off your statement balance in full each month and you'll never pay interest. I can count on one hand both how many times I've paid interest, and how much I've paid in interest. All of them were due to my own screw ups with scheduling payments ( off by a day - oops! ), however I've benefited far more from the cards than I've ever paid out. In most of those cases, the banks waived the fees anyway since there was a track record of 3-5+ years of never missing a payment, always paying in full.