Genuine question because I think about it too: On (pro) sports teams, the coach is not the highest paid. The stars make far more. I think what's challenging is that managers (and founders) are paid similar and often more than the team. I think this changes the dynamic. Is it possible the feelings relate to that as much as not building? No doubt managing is different than IC'ing, but the sense of contribution relative to pay might play a role.

A head coach also has more impact on a team's outcome than many middle managers (but probably not a founder). Managing well is hard and can be a major multiplier, but there is room at many companies to be mediocre or worse (even when trying your best) and still pass. I'm talking mostly functional managers as in Engineering Manager, PMs (most of whom are ICs) are different. Being a functional manager would be more like being the running back coach in football, the big man coach in basketball, or the pitching coach in baseball. These are different than being head coach, they help those players be good at their role, but have much less impact on the team's bigger picture. Winning in this role is seeing a player grow more than it is seeing the team win the championship. These coaches make far less than the head coach and the players.

Ultimately, I think the manager role is diminished by modern org structure. One thing said about a good manager is they block and shield—which implies the report needs protection from the org's process/structure. So a good manager runs counter to the company reasonably often. Is the manager helping or hurting the company? Both I think, but on net I don't know. It feels oddly baked into the role.