Sure but you only need to authenticate a browser once every 30 days (assuming you allow the cookie to stick around). Assuming that you are only accessing your account from a few (preferably only one or two) trusted machines, it's really not that much of an imposition.

Now, if you are checking your account from random PC's at internet cafes all over Europe, and making yourself vulnerable to keylogger attacks, you are pretty much screwed anyway. Even if you use two-factor authentication, and remember to clear out the cookie before you leave, an attacker can still steal the cookie and use it to take over your account (or at least steal all sorts of secrets from your gmail account).

Two-factor authentication will definitely help, but it doesn't protect you against carelessness.

I'm in the USA. Here they arrive within seconds.