This study discussed age-related cognitive decline, and towards the end, they describe how a sample found that a much steeper decline tends to begin at 60.
There is an active tradeoff happening here, assuming that someone continues to gain valuable wisdom in their later years of life (which is a bold assumption – some people seem to have stopped gaining it in their teen years).
Notably, one of the parts of the mind that goes into decline is logical reasoning…which I think would be pretty important for someone in such a role that we’re talking about.