This is what our document says:
"We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defence, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America."
I don't necessarily philosophically agree with a government mandate on just about anything medical either, but practically speaking, how would it not be promoting the general welfare?