That's a long and complicated story. The short answer is "we don't know". One company that hired me complained that every agile trainer they've spoken with has

That's a long and complicated story. The short answer is "we don't know". One company that hired me complained that every agile trainer they've spoken with has done a terrible job of explaining the role of management and I have to explain that's because it's one area that agile really doesn't have a good grasp of. It's a time of tremendous experimentation and we don't yet know how this is going to play out. That being said, in my training I give several examples of Agile companies that either have no management or very flat hierarchies, such as 37signals, github, Booking.com and Valve. There are many reasons why they're successful and it would be silly to simply say it's because they're jettisoning management. However, we know that large companies tend to be significantly worse at innovation (Steve Jobs is an anomaly) and they also often focus on risk avoidance rather than reward. The primary strengths of many large companies is name recognition, financial reserves, and mature products. That's very hard for smaller companies to compete against, particularly given the old saw of "nobody got fired for buying IBM/Microsoft/$insert_large_corporation_here".