1% cash back.
no fees.
no charges.
no interest.
Purchase Protection. For a good friend's birthday, I let him pick a pair of new sunglasses from Sunglass Hut. The pair he really liked was $199. Right after I paid, he set them down on the counter for a second, and then accidentally brushed his bag against the counter, knocking the glasses off, and shattering a lens. The manager made it clear that she was sorry, but she could do nothing to help. My friend looked ill over the whole incident. So I purchased another pair for him, and when I got home, I filed a purchase protection claim online. Before the next morning, AMEX had refunded the amount of the first charge.
Extended Warranty. I purchased a $300 TiVo that came with a one year warranty. 1.5 years after the purchase, the TiVo died -- simply wouldn't power on. I paid TiVo $200 for out-of-warranty service, then filed a claim with AMEX, and got the $200 refunded.
Return Protection. In the middle of nowhere on a Jeep club trip, my Jeep died and wouldn't start. Got a ride with another Jeeper to AutoZone, explained the problem, and the AutoZone employee was totally sure I just needed a new battery. Bought a new $100 battery, which turned out not to fix the problem. Tried to return the battery, but they don't accept returns on batteries. Filed a claim with AMEX and got the $100 refunded.
In regards to time, in my experience, managing cash wastes significantly more time than credit/debit. It involves multiple trips to the bank/ATM to obtain it, and the keeping/manual entry of every single receipt so that you can track your spending/budget. How freaking tedious!