Strongly disagree that an engineering manager shouldn't code; that is the shortest way to lose the respect of the team. Don't get me wrong; you need not be the "best" or the expert in all areas, but you do need to stay on top of technical developments both within and outside your organisation.
A possibly better approach is for managers to have a few side proejcts, scouting out potential risk reducing things, at a higher temperature, away from the main project. Great if one of them lands - no added problems if not. Also, if they land in the project, they are no longer the responsibility of the manager.