Employment "benefits" extend considerably outside medical cover. Speaking internationally, they often cover minimum wages, parental leave, minimum holiday requirements, pensions, often some form of income protection for long term sickness, and very often a swathe of worker rights that protect an employee from crappy employment practices (YMMV locally).
These are serious things you should not shrug off; things that make your society better. Making them optional "allows" contractors to undercut employees, but this is less a choice in practice and more a wholesale movement to a disposable workforce. Any industry with a low enough skill threshold is pushing existing employees into contractors. Great if you're a business, less if you're a single parent. You have no choice. You save no money. You just lose your benefits.
So by all means push for better healthcare systems but it's a unicorn in this context. I think you're actually —and inadvertently, I'm sure— pushing for modern day slavery under the guise of "free will". That's just where unfettered capitalism goes. I say we protect more people by recognising that they're not the ants their employers see them as. Them having rights protects us all.
Healthcare is a red herring. Ignore it.
These types of worker have no power. The supply of unskilled workers is endless and —without regulation— companies can drive conditions and remuneration lower and lower. Giving up benefits is just another cost saved for the company, not the employee.
That's why I think it's important we do regulate employment, so that people aren't having their otherwise-deserved benefits stripped away under this happy-go-lucky "gig economy" label.