All true enough, but don't forget that some people really are terrible at administrative work, and if they have enough insight to realize that they should not be chair, they should be allowed to do other committee work instead, where they will do less damage.
But remember that you would have a secretary or two to help with (guide?) much of the administration.
Only if you are really lucky. We have one and a half secretaries for a dean, chair, and a significant chunk of the college-level word processing duties (there are some folks still out there who need a word processor-er.)