The first thing noticed will be gross salary inequities since those receiving family coverage will be getting paid more that those without dependents even if they are doing the same job. We may believe that is desirable, but it would not stand in the face of competition for staff.
Second, employees would begin to understand the true cost of their benefits, increasing pressure for cost reductions that is not there now. Many will want to drop coverage or reduce the scope of benefits covered to reduce cost, forcing improved efficiency in health care.
Third, the competitiveness or American businesses within the global economy will be improved since they will not be paying health care costs. These costs are not paid by businesses in other countries.
If businesses were not paying health benefits, we would have had national health insurance years ago and health care would be consuming 10-12% of GDP instead of 16-17%.