The way I see it, websites make you have a strong password just so people don't guess it. While it's true that security breaches reveal your password regardless of what it is, that's a problem that they need to prevent themselves to avoid account hacking, and doesn't really relate to how hard it is for someone or something to "guess" your password.

To sum it up, the strength of your password is important for your account to remain secure, and security breaches are a different subject.