> People say that but it makes no sense. [...] Are you going to cut his/her salary if he leaves a big, successful team to help fix a flailing team because it has less output?

I think it works fine if we add on the concept that a good manager operates on a different timescale. The on-boarding timeline for a first-line EM can be months at some companies.

In your example, the manager moving over should be given a compensation package based on the expected value he's going to get out of the flailing team once he works his magic. (And, indeed, this is exactly the kind of package often given to externally-hired CEOs brought in for turnarounds.)

> Otherwise you're mooching off other people's work. [...] Show me what you did.

But that's just it. The manager's skill is improved utilization of resources. The leader's skill is improved direction of resource utilization. By definition, those skills are expressed on the canvas of the team they lead.

Or, more simply: A leader without followers isn't actually a leader at all!

And, indeed, we see that in the real world too: A successful executive in one company goes elsewhere, doesn't fit in with the new company's culture, and performs terribly. It's a tale as old as time.