2-factor authentication does not require the second factor every time. It typically only asks for the second factor if the device is unrecognized, or the usage pattern is unfamiliar.

So, your laptop that's logged into GMail will stay logged in when you're out of the country. Unless you explicitly log out, it will stay this way.

I enter maybe one two-factor auth code a week, if that.

So:

i) Prepare ahead and log into your services.

ii) Walk to the nearest window, get the code, and go back to your desk.

iii) Replace your phone - you keep your number - request the auth key again.

None of these are completely seamless of course, but the idea is that all of the above happen rarely enough, and are mitigable enough, that it's far better than the alternative: getting pwned.

There are also second factors in the form of mobile apps, which eliminate the need for SMS, so as long as you have data/WiFi you're set. There are also ones that don't need data at all (see: the Battle.net Authenticator, which is basically a RSA key on your phone), but require more substantial initial setup.