There's a HUGE security benefit to going this way instead of continuing to use cards. Nutshell version: as is, much of the time, we hand our credit cards to complete strangers who then go away where we can't see them to process our purchase. They bring back a piece of paper that we sign, so we give those strangers our signature too.
Mobile "card-less" model: nothing leaves your possession. Your "card" (your phone) has something brought to it so that you can establish the connection to approve the transaction yourself. Your thumbprint or password is the replacement for your signature. The "stranger" doesn't get to see a card number, name, expiration date, security code or your signature; they just get a "transaction approved" validation.
While the latter is also not completely secure (nothing is), it would be a HUGE step toward reducing the ability for the less sophisticated identity thieves (which is most of them) to fake a transaction(s) as you.
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They need to steal your thumb and/or your password too.
If you're referring to restaurants, the US could join the rest of the modern world where waiters bring portable credit card readers to your table when you pay your bill so your card never leaves your sight.