What are the benefits of becoming an academic administrator? Why do some professors choose to go into academic administration (e.g., become associate deans, etc.)? I've always assumed the main attraction is that they get paid more.

But I've also thought that if I wanted to make more money than I do as a professor, I'd just leave academia entirely and take a job in industry, where I could probably earn 30-40 percent more. I'd have less flexibility in industry than I have as a professor in terms of what I research and what my work hours are. But the same would be true if I went into administration at a university (which would probably still not pay as well as industry).

So I've never seen a real benefit of going into administration, given that the extra pay does not (to me) offset the extra responsibilities (especially when the best-paying jobs are outside of academia entirely). Are there other benefits of being an academic administrator that I'm overlooking?
I feel like I'm pointing out the glaringly obvious, but many people actually want to make their institution a better place, design policies that benefit future students and colleagues, etc.