This isn't an argument against third-party account management. It's an argument against single points of failure.
You can (and many websites which do) support multiple auth providers such as Facebook, Twitter, GitHub etc. If you bind your account to multiple of these providers, you can mitigate this risk to a large extent.
Even with that setup, people normally don't bother to associate more than one set of credentials with their account. So you would have to institute a more-than-one credential practice.
You can (and many websites which do) support multiple auth providers such as Facebook, Twitter, GitHub etc. If you bind your account to multiple of these providers, you can mitigate this risk to a large extent.