There's room for a class of contractors that do small number of hours for many different employers, either many within a quarter or many throughout the year.
One practical alternative would be universal health care.
Within our current system of insanely bad group negotiation for rates, establishing a house cleaning union that could negotiate as a class would probably be the second best alternative.
The third alternative is the Obamacare one, which is to pay your employees at a rate high enough so they can buy their own subsidized insurance on the health exchanges.
Single payer healthcare, not that your question is sincere.
Plenty of people are hired for work like that without forming a business entity, and sometimes under conditions that qualify as employment rather than contract work.
For the sake of conversation, let's consider the cleaner to be an employee and OP to be the employer. Even then, unless OP has 50 full-time and full-time equivalent employees, there is no requirement for the employer to provide group health insurance, according to the ACA.
Obviously if she only has one client that’s not going to be a lot, but it stacks with all the other employers
You would never be obligated to pay for their health insurance, it would be up to them, or their employer, to figure that out.
Walmart on the other hand has clear employees which are expected to turn up to non-negotiable shifts and wear a Walmart specified shifts. They’re currently forced to take on the risks of a contractors, but with none of the freedoms.