Why do tenured professors at high-ranked universities move to lower-ranked universities?

There are many reasons that people change institutions. I was tenured at an R1 institution and moved to a "high research" institution because I wanted to live in the area where the second institution is located. Although my current institution has a lower research ranking, it is the state's flagship school, where my former institution is not. So, I actually get more resources, better pay, and our students are more prepared when they start college, compared to my prior institution. So, your assumption that a higher ranked institution is better is not always true.

A very common robust pattern I see in engineering faculty (aspirational types):

Tenured at (say) Top 10 -> Move to Top 20 and become department head -> Move to top 30 and become Engineering Dean -> Move to top 50 and become president.

Another reason to add to the list: A university that wants to grow a department (including in reputation) has to start somewhere. That somewhere may be by headhunting talent. They have considerable leeway in salary and more in other resources: promising a million gold pieces to set up your lab, 3 postdocs and no teaching for 5 years would be quite attractive.