To prevent this from leading to rampant inflation the US passed laws that regulated wages and prices, such as the Emergency Price Control Act of 1942 and the Stabilization Act of 1942.
Insurance and pension benefits were not counted as wages, and so employers that could no longer legally raise wages to get people people to come work for them instead started offering health coverage.
Americans, who before this had largely been on their own when it came to healthcare, liked this, and so even after the wage controls ended unions bargained to keep those benefits and over the next decade or two expand them to include vision and dental benefits.
By the early '60s it was clear that there was a serious problem inherent in this. Employer sponsored health insurance had become that basis for nearly the entire American healthcare system. People who then left that system such as when they retired often found they could not afford to buy their own insurance. And so Medicare and Medicaid were created to try to handle people who could not get employer provided health insurance.
We almost got major healthcare reform in the early '70s. Senator Kennedy proposed a single-payer system that would be available to every American. President Nixon proposed a system that pretty close to the ACA (aka Obamacare). Then Watergate happened and pushed healthcare reform to the back burner were it sat for around 40 years.