> 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 payments or you are out dining with friends, and another day not at all.

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