Why pay the insurance company's admin costs for taking premiums and billing customers (with entire departments seemingly dedicated to refusing cover), when all that paperwork would be redundant if the hospital provided the treatment unbilled at the time of need (so no need for a department to track the itemized cost to the 'customer', or any need to bill the customer, or indeed any need to exist at all) funded in bulk through tax (so if you earn more you pay more, but it's still less than insurance because nobody pays for all that unnecessary paperwork), and there's enough left over to pay for e.g. maternity care.
In short keep the hospitals and doctors, but ditch the insurance companies which bring nothing of value.