What problems with paying with credit card are solved with paying by phone?

You can loose both, you can forget both, Also credit cards are water proof, drop proof, have no battery issues, no network connection issues. Even though you could leave your credit card at home you still need to carry your drivers license, work badge, grocery discount card, student id, gym membership card, atm card in case you need to get cash, make up, car keys, so what if you have to carry an extra card.