> convince a user to enter their google 2fa code into a site that isn't obviously google?
if the BAD site itself looks legit, and has convinced a user to do the initial login in the first place, they won't hesitate to lie and say that this 2-factor code is part of their partnership with google etc, and tells you to trust it.
A normal user doesn't understand what is a 2factor code, how it works, and such. They will easily trust the phisher's site, if the phisher first breaks the user and set them up to trust the site in the beginning.
What google does is to send a notification to the user's phone telling them someone tried to access their account if this happened (or any new login to any new device you previously haven't done so on). It's a warning that require some attention, and depending on your state of mind and alertness, you might not suspect that your account is stolen even with this warning. But it is better than nothing, as the location of the login is shown to you, which should be _your own location_ (and not some weird place like cypress!).