It's for online payments only. You click on the wero button on a website/app, if on mobile takes you to your banking app (on desktop, you scan a QR code), you do MFA on your banking app and confirm, and the payment is done.
Wero are not in the business of issuing cards, though obviously they could get into that business - just like UnionPay did in China. I suspect there would be a lot of inertia there, as card payment fees are capped in Europe anyway.
Cards are also online payment. You can already pay with such systems in some physical shops and restaurants, alongside google/apple/alipay.
But cards are offline from the perspective of the consumer. Sometimes even on the merchant side of things. Not that it is an important distinction nowadays--but I have definitely tried to pay with a merchant's own app-based payment solution that refused to load due to a bad cellular connection. I haven't looked into how Wero will handle this.
Most payment terminal nowadays use 4g network and it is not uncommon to see shop/restaurants employees in some areas trying to desperately get a signal by moving the terminal close to the door or window.
They need much much less data than your phone. They could process several transactions with less data it would take for your phone to load the HTML of the payment page, let alone the Javascript or the bank's logo.
Also, such terminals often use multi-carrier data plans that can use the best carrier available, while your own phone is stuck with one of the options (of course, you always have the worst one).
Wero bought Payconiq which allow to pay at the physical terminal with a QR code to scan with your phone. So, they can cover the physical payment without having to issue cards.