Even under single payer, the insurance companies will thrive. Nine out of every 10 Medicare recipients have supplemental private insurance to cover costs that Medicare, a single payer system, does not cover.
The insurance companies are not going to be shuttered. And single payer is probably inevitable because the public will eventually demand it as Obamacare fails. With only 40% of doctors accepting Medicaid patients and more and more doctors not accepting Medicare patients, I can see a public outcry demanding that doctors and hospitals must accept all Medicare and Medicaid patients despite the low reimbursement rates. Just like the annual "Doc fix," the reimbursement rates will be raised and then we will go into single payer.
They will outlaw supplemental private insurance.