I could, but since I'm already paying for it in taxation, why should I pay for it again?
The government monopoly on force crowded out the little guys.
I live in a country with free healthcare. Yet there are many people who buy private health insurance, including me. They provide services that are of value to me, so I pay double. So obviously the services that you described weren't valuable enough. Bluntly put.
The services I described were undertaken by the poorest, with the least disposable cash. The friendly societies were not run by the rich. Who had no need for it.
The idea that they would pay their additional tax
and continue with their friendly society for the same safety net is ludicrous.
Just as today it is not the poorest who buy additional healthcare cover.