You can do this.
First, you need to have reserves equal to the medical costs of one person for two years. These reserves must be liquid, meaning they must be in a bank and that you can get to them easily. The average healthcare spending in 2016 (the latest year available) was $10,345 so you'd need close to $21,000 in reserves.
It also takes several years to go through the paperwork and get approved, so you'd probably close to being out of college by the time you were able to sell a policy to yourself. Of course, before you sell the policy you'd need to be licensed in your state meaning you must take and pass the test.
You'll also need to pay a lawyer to draw up those papers and then take them to the state to get approved. You could put that same lawyer on a retainer (which will cost more money each month) in case you get sued by yourself or one of the doctors that you contract with.
With everything else that you'll need the cost will probably be up around $100,000 just to do this for one person. Of course a real insurance company would be paying $50 or $60 million to get started so this would really be comparably cheap to do.
So this idea, while possible, isn't feasible.