They should offer an incentive. "Get a cotton swab painfully shoved up your nose, and if the virus is present, you're grounded for two weeks!" might not be the best motivator.
It's not that people completely lack altruism and will never do the right thing for its own sake. Most people do the right thing most of the time. But it is not a good idea to rely on altruism from everyone.
In NYC, they send you a COVID care package if they trace your positive. They send things like masks and hand sanitizer. Instead, they should give that to you so you shouldn't get COVID. Also, they send you masks so you should go food shopping and not starve. Instead of making people with a virus spread it to others, they should arrange free food delivery to homes.