[drivebyacct2]

Google already does this with Chrome and Google websites.

I don't have to enter my second factor with credential or even my password when using Gmail from my phone, tablet, laptop or desktop.

[natrius]

At this point, I actively seek out Google account login options. It is so incredibly pleasant to use on Android.

[stcredzero]

Yes, but I'm not so sure that's really two-factor authentication.