I mean if you replace "taxes" with "profits" you have the current American healthcare system. Condemning people to die from a lack of treatment in order to save on profits.
Meanwhile private insurers definitely deny coverage to people with chronic illnesses (not everyone who is sick or dying is on Medicare/Medicaid). In a single-payer system those folks wouldn't slip through the cracks and .... the doctors would be incentivized to keep them alive! (assuming doctors are profit-motivated sociopaths like your average HN poster)