Self-employed people are in the same demographic as other individuals without any access to group insurance, such as those working lower-end, lower-paying jobs. As a matter of sheer statistics, a larger proportion of this population ends up sicker and incurs greater medical expenses.
Something similar to what your grandmother had or other unions is a PEO, or professional employer organization. It's a collection of small businesses (usually) that band together to get access to services otherwise only available to larger groups. It's a little interesting because technically you become an employee of the PEO as well as your own company, and there are certainly costs associated with it, but it's in the same vein as union dues, for example. Just not as clear cut and not required.