Yeah and we’ve seen that fail again and again and again. So no.
How do you define failure? When did "again and again" occur? I don't see that you have any valid argument or any supporting data whatsoever. Private health insurance exists and works.
Insurance doesn't have to cover everything: any aspect of coverage is debatable since it is a contract between buyer and seller with the courts as the deciding powers when either buyer or seller believes the contract has been violated.
Let private businesses sell insurance. Let people buy what insurance they desire.