Earlier quoted context omitted.
NemID, the previous national 2-factor solution, used a small card with rows of pre-printed single-use codes. When you logged in to a bank or a public sector website, it would ask for a random code at a specific row and column number. Once the system registered that you had just a handful of codes left, a new card would be sent to you via snailmail. It worked fine for the time. The current system, MitID, depends on sm…
The big drawback of one time passwords is that it doesn't protect against man-in-the-middle attacks such as phishing, which is in practice one of the most common attacks on systems of this scale. The logistics operation involved in distributing codes is also very expensive and inflexible. You may need to authenticate payments a dozen times in an hour one day, when you are on a farmers market which doesn't take card p…
Neither of the scenarios you describe would require you to authenticate using MitID: Peer-to-peer payments in Denmark are typically done using the app MobilePay, which only requires MitID authentication during setup. And you never need MitID authentication when paying in person, at most you'll need your card's pin-code