Integrity is important and missing. I think there's a contradiction in what you're writing though. Recognizing the importance of personal and social relationships is what's keeping the no integrity people around and/or getting them promoted. It's the networking for networking sake as well as the more mundane social lubricating they do in contradiction to integrity. It's disagreeing with discussions, projects, companies, leaders and going along with it and expressing agreement. It's smiling, being "enjoyable to be around", being naive or presenting as naive, and being easy to work with. And more specifically being easy for the many liars and sociopaths to work with. Caring for personal and social relationships is not inherently reinforcing of all that is good. I wouldn't know how to count, but I feel there's quite a bit of it reinforcing the bad.