Of course none of it will affect the abilities of an actual leader, but the perception problem cannot be dismissed. Not having the above doesn't mean you cannot be taken seriously as a leader, but it does change the approach.

A person will get real damn frustrated if all the advice they get works for one segment of the population and doesn't work for them. That can cause all kinds of self doubt and depression. You need to be able to honestly assess how other people perceive you and work on strategy, skills, and maybe some changes in physical activity to have a good outcome. I just hate to see people get depressed when they shouldn't.

I agree with you, these qualities are not intrinsic to leadership. But subconsciously (or perhaps consciously), others see someone who is healthy, vibrant, and well-groomed and, knowing nothing else about the person, they will infer that this person is in control of their dietary habits, fitness, and hygiene. It's easier for someone with the appearance of health to convince others that they are a leader than someone who appears sickly or behaves slovenly.

Again though, like you said, it's not intrinsic. No one would argue that Churchill was not an excellent leader, even if they did disagree with his politics or his methods.