Those are roughly my thoughts as well, although I'm afraid that I only believe this to rationalize my decision to go into academia. While the argument makes sense, there are definitely professors that express frustration with their position.

What does seem like pretty sound logic is that if you could get better results without a research group, you wouldn't form a research group. So you probably won't run into the problem of achieving suboptimal results from administrative overhead (you could always just hire less people), but you might run into the problem of doing work that is less fun than it could be.

Another point is that plausibly some other profession (corporate work?) would have less administrative overhead per unit of efficiency, but I don't actually believe this to be true.