"Small-group" coverage is generally 50 or fewer (in some states, 100) members:
https://www.healthinsurance.org/glossary/small-group-health-...
Otherwise, the socialised version already exists, in most industrialised countries, in some form or another. Within the US, Medicare for the elderly, Medicaid for the poor and children, and in many states, "high risk pools" which are state managed.
More generally, a problem is that the bulk of health benefits do _not_ accrue from direct or acute medical treatment, but from public health and preventive measures, _especially_ well-mother, well-baby, early childhood, municipal sanitation and environmental measures, and general (workplace and elsewhere) safety provisions. Insurance companies of and by themselves don't address much of this.
Adverse selection is the big reason. An individual signing up for insurance can be used as a signal that means "individual is sick" or "individual is likely to need insurance soon". If a company policy covers all employees (or all employees above a certain level), the signal is "person works" which is orthogonal to "person will need insurance" (in fact, it's probably slightly anti-correlated, a.k.a. "person is fit enough to work").