If nothing else, those human connections can be the difference in outcomes when you inevitably screw up. If you've invested in relationships, when you make a mistake, it's more likely someone will say "bluefirebrand means well, and I can see how their good intentions led to this outcome. Let's figure out how to fix this so it won't happen again to them or anyone else." If no one at work knows you except as the person who sits off to the side and never talks to their coworkers, the response may very well be "bluefirebrand who? Alright, let HR know we need to hire a replacement."

Again, it ought to be the case that none of that matters, and everyone is treated the same regardless of their personal network. But it is the case that this isn't how the world works, and it's not reasonable to wish it otherwise. I mean, are you as likely to help a stranger as a friend even if their needs are identical? Most people would say no.