Admittedly, there are several advantages to linking networks. First is just ease and effort - i.e., it saves time and is convenient when posts on one network get automatically reposted on another network. Actually, to my mind, this is the primary benefit. It get maximum social network exposure for my effort. However, a related advantage is access. I may have access to some networks from a particular device but that access is more difficult from another device. Similarly, I may be on a particular network (at work, at school, etc.) that has access to one social network but not others. In either of these situations, my access to one social network will effectively be extended to others if, behind the scenes, those networks are connected for posts to be re-shared automatically. This leads to a third advantage which is usage of your data plan and related cost. When social networks are connected together for my posts to be shared (usually determined by your profile settings), I only have to upload a photo to one (and only have one usage of those megabytes on my data plan) to get that photo onto several networks. Separate posts would be separate transmissions of the same photo which is a double hit to one's data plan.
But there are disadvantages as well. An accidental, ill-tempered or you thought it was funny but it wasn't post on one social network will be a mistake that is rapidly replicated onto other social networks. Formatting can also be a problem - i.e., the appearance of your re-post when done by a back-end integration of two social networks may not be as pleasant in appearance as if that post uses the posting tools optimized for each network. Finally, there is the issue of access control. For the most part, posts that can be automatically shared between social networks can only be if the posts are both public on those networks. Increasingly, privacy conscious users of social networks will not want to make public posts but favor using groups and to do this almost always posting to each social network separately.
For a time I was a great fan of linking social networks. It was certainly convenient. In the earlier days, it was also technically interesting to figure out how to do this as it usually involved some "hacking" together of web services, RSS feeds, and the like. But, more recently, I've disconnected my social networks as I favor posts that take better advantage of the tools in each social network platform and as I've become more conscious of how to use groups or other privacy settings.
If you have thoughts or insights on this topic, would love to hear those. Please leave comments below.