The problem is not that a phone is fundamentally better for this stuff, the problem is that you're yet to be provided a card-based alternative that works well.
For transactions under $100, card payments in Australia don't require authorisation (I'm unsure if this is a legal requirement, or if it's just a de-facto standard that most of our banks have adopted). You just wave the card and you're good to go - the payment processes using the same mechanism as tapping a phone so it's just as fast.
It's actually more convenient in most cases as many places don't have their credit card terminals right in front of where you're served, so the cashier has to walk over to a terminal. With a card, I hand it to them and say "just tap" - they handle the rest while I wait and talk with whoever I'm with (or check my phone if I'm on my own). With a phone, I'd have to walk over to the terminal, wait for the cashier to key in the pricing and then hope that Touch ID won't stuff up while I hold it near the contactless reader. I also can't check my phone while I'm doing that, because I need to use it to make the payment.
Tapping cards works so well and is so widely supported that I was able to live just fine with a near-destroyed debit MasterCard (and zero cash) for nearly six months a few years ago. The plastic was coming off and prevented it from being inserted into a terminal, but by 2012/2013 our retail sector had such widespread support for contactless payments that it didn't matter. For the purchases over $100 I made, I tapped and then entered my PIN.
Despite Australia being the highest users of contactless payments in the world (per capita, of course), Apple Pay has had a very slow launch here. It only works for Amex (which no one uses as no one accepts it due to high fees), and MasterCard/VISA cards for one of our big four banks. The banks aren't interested in dealing with Apple due to extra fees that Apple wants to impose, and consumers aren't pressuring the banks or Apple to make a compromise because the current experience is already good enough.
Maybe there's something "magical" that I'm missing out on, but I really don't get why phone-based payments are being so widely hyped. It's already a solved problem.