As it is right now, my cell phone replaces a collection of about six plastic cards. I have not yet found a wieldy phone case that has space to store payment cards.

Realistically, this question could also be asked with cash. If you're going to be pulling out a wallet-like item anyway, and you are that concerned with privacy, why not go with anonymous, fee-free, secure, actually offline paper money? Card processing is not offline. The card machine has to be connected to the Internet for it to work (offline card processing theoretically exists, but is not widely implemented enough to rely on and is not particularly secure).

If people are going to argue that wanting to pay with a cell phone instead of a plastic card makes me lazy because the card takes a few extra seconds to use compare to the phone, I'm going to argue in turn that they're lazy for using a card when using cash, with all of its privacy benefits, also only takes a few seconds more.