We provide physician care because injury and illness are social negatives and a threat to the body politic. Dealing with negatives is what we hire agents of government for. Providing for health and welfare is a Constitutional obligation. All Constitutional obligations have to be carried out regardless of the personal characteristics of the recipients.
While the amendments to the Constitution are commonly referred to as a Bill of Righta, they, along with the whole document, are addressed to the agents of government, not the potential recipients of services.
Just as the Ten Commandments are not addressed to God, the Constitution is not addressed to the people who govern. Why is that so hard to understand? Because there be segregationists among us who are bound and determined to identify some population that can be excluded/abused with impunity. Why is that their ambition? Because it gives them a cheap thrill. Effortless Potency.