The problem I've had with U2F is that it mostly works nowhere but Chrome, AFAICT. I guess that would be fine, except that U2F doesn't work on Chrome on my platform (FreeBSD, where it causes a segfault).

I tried for a while to run U2F on firefox with an extension. However, I was forever fiddling with user-agent switchers, as I'd only be offered U2F if I was masquerading as Chrome. And even that didn't seem to be enough to use U2F with Google, the last time I tried.