The reason Americans sue is because they have private health insurance and astonishingly expensive health care. If an insurance company decides responsibility for an injury or illness can be blamed on somebody else, they will force their client to sue that person. People's names are on the court docket, but the litigants are the sick person's insurance vs the blamed person's insurance.
The sick or injured person could refuse to sue, but if they do so, they could lose access to further medical care and go bankrupt. Hospital treatment for a broken leg can cost as much as several months wages. Most people would rather not sue over tripping hazards, but they have no right to treatment if nobody pays.