I had always been skeptical
But I found a particular case paying via Apple Pay is a timesaver for me. My grocery store has rewards that pay in cents off for gas - and it basically works out that with me needing to fill up every 3-4 weeks I get free gas (well 0.9 cents per gallon) on each fill so it is worth doing.
I won't carry loyalty cards but they support Apple Wallet so I scanned in the card and can show them my phone and they use their little laser scanner on its QR code just like they would if I carried the card. Since I have to get my phone out at checkout anyway, paying via Apple Pay saves time over pocketing the phone, pulling out the wallet, taking the card out, and waiting for the frustrating long "authorizing" time the new EMV cards require.
In fact the authorization time is long enough it probably IS quicker to use Apple Pay (or Android Pay) than to use an EMV card. Its just a matter of not easily knowing where they are accepted, since the readers aren't always marked with the logo and I'm not going to hold my phone near the terminal just to see if it works. The fact payment is as anonymous as cash (at least for Apple Pay, with Android Pay not so much) is nice too. I may be willing to trade my privacy for free tankfuls of gas, but that's my choice and for most purchases I don't see any reason they should get to know my name.