I disagree about the mental exam. Trump took one and released the results. Biden should do the same, because it's the right thing to do.
I think if he and his team knew he would pass it with flying colors they would absolutely release the results.
No matter who it is that undergoes a 'mental' (do you mean cognitive) exam, who is to say what is released following it is accurate or even truthful, particularly what is released to the media? When a president takes a cognitive exam, exposing that he or she is in serious cognitive decline is a security risk for the country. Our enemies might take this as being to their clear advantage.
This likely will never happen, but there should be either age limits or a mandated physical and mental exams prior to folks being nominated for any important political office to help ensure they can do the job and to assist the voting public in choosing the most viable candidate.
Also, once someone is elected to office, they should be required to have a complete health exam annually. This should also be a requirement whenever a deficiency is reasonably suspected.