Is it sensible to use application password bypassing two factor authentication?

I discovered that some applications (like Sylpheed) seems unable to support two factor authentication.

Google has a feature called application passwords - a separate password that "grants complete access to your Google Account".

Maybe I am missing something, but it seems to completely negate any benefits from enabling two factor authentication. Attacker again needs only to break a password.

Is it sensible to enable two factor authentication and then create a separate password that bypasses it?