I would guess the type of project and the team plays a role as well. If you have as a captain a capable first and second lieutenant who can execute on your directives, the 100 man regiment will be very effective. Much more effective than with the captain spending most of his time in the saddle.

In other words, if the manager has a team with a good mixture of senior and junior people, he can fully focus on the management. He does not have to understand the implementation requirements.

If the corporate culture requires a lot of political battles, being a manager is a full time job. To fight for funding, be not killed by another department, get revenue recognition sorted out.

And if the team consists of all juniors or worse, all seniors with different opinions, without the technical skill the manager will make random decisions - whoever presents his opinion best today.