That would be very expensive for very little benefit - five minutes is more than long enough for multiple people to use the same buttons at a busy hospital during the day.
It's much better to promote behaviors like washing hands before touching food or mucous membranes (like rubbing your eyes) and using alcohol-based hand sanitizers when that isn't practical. That's why you see hand sanitizer dispensers every few feet at (good) hospitals, and why infection rates plummeted when hospitals introduced them.
In addition, never touch those buttons with the tips of your fingers. Use the knuckle of your pinky instead - it's much less common to accidentally use that to touch a mucous membrane later on, so it's slightly better.