Paramedics are not afraid of riots nor fights. They are useful for healing mass amounts of people in a short duration of time without having to buy an excessive amount of doctors. They can heal both staff and prisoners.
Paramedics will remain on the compound for several days, so many use it as a temporary solution for healing, if the bureaucracy research or infirmary with doctors is too costly, or when your own medical ward has too much to deal with.
They were added to the game in Alpha 10.