Can you imagine a physics department where the chair is on administrative leave?
Easily, with an interim acting chair. Upheaval under all contingencies is minimized with this solution.
Yes why is it any different to any other job - the deputy does the job,
Can you imagine a physics class taught by a grad student?
Half the job of the chair is to manage the human side of the department's priorities, including resolving disputes between faculty. You need moral authority, which a grad doesn't have.
The scale is about the same, and as someone else mentioned near here, the deputy chair would take over.