Siting a treatment and disposal facility is challenging. Many factors come into play, including:
NIMBY - “not in my backyard” is a society-wide quandary that plagues waste management. People want the goods and activities that produce waste, but they do not want the waste treated or disposed of near them. When you put the adjective “medical” or “hazardous” or “radioactive” in front of waste, people get even more antsy.
Further if the treatment is an incinerator, imaginations run wild with ideas of bacteria-laden dust settling on their homes.
There are some legitimate objections to siting of medical waste facilities, as they tend to be located more often in low income areas. The concept of environmental justice comes into play. The EPA defines it as "the fair treatment and meaningful involvement of all people regardless of race, color, national origin, or income, with respect to the development, implementation, and enforcement of environmental laws, regulations, and policies."
This is a worldwide issue, and waste often crosses national boundaries. Indeed, the Basel Convention is about trade and transfer of waste.