I think the larger the team, the larger the managerial workload. We're so small, if our client app manager stopped doing dev, we'd have to hire another person. At a global company I started with after college, working with with a team of 10, my boss split his time between managerial busy work (expected of him by upper management, not self-imposed) and being as involved as possible. He was always able to speak intelligently about the product and its code, and was able to contribute in ways that set an expectation of quality. He always had the respect of the team (and when not, someone got fired). I consider him to have been a mentor - he got it right.
If you're managing a team of 40, being involved directly in code/execution is likely impractical and perhaps even detrimental, but at any scale up to 15 people or so, direct involvement seems both practical and necessary to retain the respect of your team, and assure a quality product in the end.