Brooks' law is not actually a law of physics though.
There is a lot of wisdom to it. But there are good ways to add resources and bad ways. Perhaps a team isn't getting help from another group. Perhaps there are some tasks that others could offload in a way that doesn't distract the team on the critical path, etc.
It's a good adage but it doesn't mean that you can never take steps to accelerate project delivery.
You seem to have a rather negative view of managers.
In my experience, good managers can be quite valuable negotiating with other organizations in the company and with getting needed resources. In fact, I'd say that's a pretty significant part of their job.
There is a lot of wisdom to it. But there are good ways to add resources and bad ways. Perhaps a team isn't getting help from another group. Perhaps there are some tasks that others could offload in a way that doesn't distract the team on the critical path, etc.
It's a good adage but it doesn't mean that you can never take steps to accelerate project delivery.