The idea behind flattening management structure is supposed to make employees more productive by making them feel as if they are part of the decision-making process, and streamlining both customer and personnel feedback by removing layers of middle-management. That's the idea.
In reality the most personal relationship I have with anyone in my management chain is my direct manager, whom I report to. He knows my strengths, my weaknesses, and the team dynamic - who works well together and why - which team members are more adept at which tasks. He personally juggles and doles out tasks based upon this knowledge and planning for future tasks. What it has always come down to for me is nurturing that relationship - attempting to work closely with the one who both writes your annual review and who's eyes you have to meet when you fail. And that's what it comes down to. Context. That very personal relationship you have with your first-level supervisor no matter your level.
So while horizontal organizational structures are all the rage, severing my personal relationship with a real person and placing me under a remote manager I'll never meet in another part of the country is not going to foster a close relationship. Its not going to make me feel more productive nor part of the decision-making process. My annual performance review will now be written by someone who's eyes I don't have to meet, and both of us will suffer for that.
Or, like I told him when he called to introduce himself, "I have been unimaginably successful every time I have had a local, on-site manager. The inverse has been painfully accurate each time I've reported to a remote one."