I'd like to start by saying I agree with you completely, except for one little thing. A disability is occasionally a limiting factor.
I'm not speaking to either of the candidates, but hypothetically. Also, I'm going to exaggerate for the sake of clarification. Let's say hypothetically that you run a daycare, which is a pretty good metaphor for being President BTW. And let's further suppose that while hiring for this daycare, you are presented with two candidates who are essentially indistinguishable, except that candidate number two occasionally hear voices that tell them to harm children. The law says that both candidates must be given equal treatment, but wouldn't it be better for the second candidate to go get medical help, instead of being placed in a position where he or she might actually harm others, and by extension themselves?
The complete disclosure of medical histories is probably too much, but the disclosure of medical issues that might directly affect their ability to perform the job, like dementia, or Alzheimer's doesn't seem like an excessive request. Physical health conditions are essentially irrelevant. One of the three best Presidents the US ever had was in a wheelchair. But previously diagnosed mental issues should, in my opinion, be subjected to public scrutiny if they would affect the ability of the person to correctly perform their job.