I can already buy something with one click on Amazon.com from my laptop and desktop. And have been able to for some time. Adding that feature to a mobile phone will help, certainly, but that alone would not make a better shopping experience in my mind. I would still have to have that company's app, or browse their site in my mobile browser, which will always be slower than using a full fledged laptop or desktop.
I agree that if someone could make purchasing simpler on a phone than on a laptop/desktop (possibly through NFC or something) then it could be a preferable approach. But just storing credit cards isn't going to cut it in my opinion.
I think the difference here is that I'm already on my phone or iPad looking at the item in the first place. It's a pleasant experience for me to look up things that I might like, or to grab something I know we need. Oh, we're out of light bulbs? Pull out the phone, Prime them, done, don't need to think about it. It's not that it's easier on the phone/tablet over the laptop, it's that more and more those devices are becoming the first thing I go to.
I agree that if someone could make purchasing simpler on a phone than on a laptop/desktop (possibly through NFC or something) then it could be a preferable approach. But just storing credit cards isn't going to cut it in my opinion.