From my point of view, the usage of social logins makes only sense if you use some kind of functionality. If you just use them as container, so that the user doesn't require to create a new user / password, it leeds to a strange feeling for the user: "why should I connect my Facebook login to the site, when the site must not use any information from my Facebook profile?".
Regarding the "only if the site is social" I do not agree. As I mentioned above, you could make usage of the social platform in your application, then a combined login would make sense, even if your site is not a social platform or similar.
Keep also in mind, that by using some services as login provider, the application must ask the user for access to certain resources (e.g. allow the application to post on your timeline, ...). If this is wrong configured, it could prevent user from using your service, as they do not feel comfortable to let the application get control over certain part of their social profile.
All in all if you add them, I would all the time provide a normal way to login (e.g. create a new login to store the data). This provides an alternative way if a) someone doesn't have any social login
b) the user would not like to connect the social service with your application.