One of the problems here is that few sites support U2F, and even fewer support it properly. Proper support would mean allowing multiple tokens, so that you can

One of the problems here is that few sites support U2F, and even fewer support it properly. Proper support would mean allowing multiple tokens, so that you can have one permanently on your keychain, one permanently in your computer at home, and an off site backup pair that you rotate (enroll the one that is at home, then swap and enroll the other one). On desktop, touching a U2F token is a lot easier than typing numbers from a SMS, and it actually protects against one of the biggest threats, phishing (the SMS does not - if the phisher bothers to ask for it, the user, who thinks that they're logging into the legit web site, will enter it).