There is no "remembering" involved -- you get the second password from an app on your phone. And you only have to enter this second password once per month (per computer that you access your account from).
I assume you enter the second password once per browser session, not once "per computer." For people who use incognito mode heavily or clear their cookies on shutdown this will mean using the second password every time, but something tells me those people are of the type who want to be using two-factor auth all the time anyway.
