There are multiple ways to get insurance without dealing directly with traditional insurance companies.I'm not saying they're perfect, but then again, neither is the current for profit.
Many large companies will “self insure” by negotiating deals with insurance companies to isolate their risk pool to their own employees. Since employee demographics are relatively homogenous compared to the general population (younger and healthier generally), large companies can offer a “win/win” in partnership with insurance companies by capturing actuarial efficiency through more precise modeling of their risk pool.
Many large companies are self-insured. They still contract with an insurance company to provide benefits management and customer service. Even if you are self-insured, you still want to take advantage of negotiated rates with a network of providers, which today comes from insurance companies and/or HMO’s.
I don't understand your point? These examples would have to either provide care or have contracts with providers. Cigna and your examples provide access to their networks for a management fee (where your company pays the actual costs)... So we are both calling tomatoes, tomatoes.
Christian Health Ministries - http://www.chministries.org/ Medi-Share - https://mychristiancare.org/medi-share/ Kaiser Permanente - https://healthy.kaiserpermanente.org/
Taylor University is self-insured.