TOTP is in terms of usability not very different from PhotoTAN or ChipTAN, so I don't see how these methods aren't "proper 2FA".
U2F is a useful method, but it's not common at all (even in IT most companies don't provide it, not even the website we're on right now, nor PayPal), and it's not understandable how this isn't "proper 2FA".
In addition, the directive requiring the purpose of the code to be fixed and shown aside it, either in the app generating it, or in the push notification, is a very useful security aspect which most other 2FA solutions miss — even U2F can't differentiate between a login and a transaction authorization.
I don't like TOTP. U2F, however, is both convenient and secure. You touch a dongle, you're in, and at the same time there is no way to get access to your account without physically stealing the dongle. It's a proper second factor to a password.
Other solutions are either or. There is a benefit to confirming particular actions (with the info about the action) in the app but it's unnecessarily inconvenient for mere login.
U2F isn't widely supported but I managed to secure virtually my entire high-value Internet presence with it. Google, OVH, Coinbase, and Stripe all support it. Let's be honest, for HN I wouldn't bother with any second factor. I have the password saved in the browser and that's more than enough.
U2F is a useful method, but it's not common at all (even in IT most companies don't provide it, not even the website we're on right now, nor PayPal), and it's not understandable how this isn't "proper 2FA".
In addition, the directive requiring the purpose of the code to be fixed and shown aside it, either in the app generating it, or in the push notification, is a very useful security aspect which most other 2FA solutions miss — even U2F can't differentiate between a login and a transaction authorization.