Is that something that happens often?
I'm not sure how we got from manga to implanted credit cards, but personally, if I'm going to engage in any retail consumerism activities, step #1 involves driving to the store in my car. For that, I'm legally required to carry my driver's license (which is in my wallet, along with my credit and debit cards), and unless I just want to stand in my driveway and stare blankly at my locked car, I also need my keyfob (which is on my keyring). Technically, I could leave my smartphone at home but then I'd have no navigation or music (aside from terrestrial broadcast radio, yuck) in my car.
So, when I arrive at my shopping destination, I've got several different ways of paying for things just by virtue of all the crap I've had to bring with me anyway out of necessity. There's no way I'd ever want to go under the knife to solve a problem that isn't actually a problem. Plus, on more than one occasion I've placed an in-store pickup order while I'm already at the store, and all I needed to pay for that was my username and password, which I have memorized. It seems barbaric to perform self-mutilation as a workaround for stores that can't just process payments via a simple account login, if someone really insists on not carrying around other forms of payment.