It's not that easy, luckily, if you're self-insured and have to take the service of a doctor, you can't switch just like that. It takes about a year of paper exchange with everyone involved to switch cleanly. Even then, any costs you started paying for from before will still have to be paid unless you're below a certain income bracket (or declare bankruptcy).
So if you were self-insured and broke a leg, then decided to switch back to insurance, you'd still be on the hook for the costs of the ongoing physiotherapy until it is healed back up. The insurance doesn't have to actually pay anything that happened before a switch (switching from public to public insurance or private to private doesn't have this limit, private to public and the other way round but you don't pay, your old insurance pays).
So if you were self-insured and broke a leg, then decided to switch back to insurance, you'd still be on the hook for the costs of the ongoing physiotherapy until it is healed back up. The insurance doesn't have to actually pay anything that happened before a switch (switching from public to public insurance or private to private doesn't have this limit, private to public and the other way round but you don't pay, your old insurance pays).