People without insurance still go to the ER and then simply don't pay the bill. When the hospital needs to recoup that money, they raise their prices. When they raise their prices, they charge insurance companies more who then pass that increase in cost onto you. You're paying for that person's care one way or another.

In addition, by driving people further into debt and a lower socio-economic status you're indirectly increasing crime. You pay for that through increased taxes for police, prisons, etc.

By making healthcare a right, you would then have the right to tell any doctor around to to work for you at the threat of a governmental gun.

This is objectively untrue and a straw-man for two reasons. (Note that my wife and brother are both MDs with specializations and combined have more than 30 years in various levels of medicine.)

The ER already cannot turn patients away meaning doctors working in the ED currently have no choice on who they see. Additionally, most doctors working for hospitals are either assigned patients (meaning they have no agency in choosing their patients) or are called for consults by other doctors working in the area. While they could always refuse a consult, it's generally not done unless it's medically unnecessary to see the patient.

Secondly, private practice doctors will always have the ability to turn away patients because it's a private business. Healthcare being a right doesn't change this. For evidence of this private water companies still exist that profit off of slave labor (Nestle).