If a mentally incapacitated president is impeached shouldn't he go to a mental institution for treatment? How does he get better?

We've only had two mentally incapacitated presidents. Lincoln fought depression all of his life and Clinton had an over active libido. Since Clinton dodged removal from office, I supposed that gave him a pass as far as seeking treatment goes. Your implication about Trump wasn't lost on me, it's just that I categorize it under the heading of wishful thinking and let it ride.