How is receiving the council of an attorney a right (at no cost if you can't afford it) while receiving healthcare is not a right?

Obligatory disclaimer: I'm not a lawyer, and I have no legal training.

This question confuses a "right" as granted by the legislature or the courts with an inherent right.

The Right to Counsel results from Supreme Court interpretations of the Constitution, relevant case law and their applicability to the Miranda warning. It is not an inherent right, and thus (I would argue) not a right at all, and for the same reason a "right to healthcare" is not an inherent right.

The Miranda right to counsel is a faulty application of the 6th Amendment right to "the Assistance of Counsel".

"In all criminal prosecutions, the accused shall enjoy the right to a speedy and public trial, by an impartial jury of the State and district wherein the crime shall have been committed, which district shall have been previously ascertained by law, and to be informed of the nature and cause of the accusation; to be confronted with the witnesses against him; to have compulsory process for obtaining witnesses in his favor, and to have the Assistance of Counsel for his defence."

This has been interpreted to mean that the state must provide counsel, rather than to mean that the state cannot DENY counsel to a defendant.

In short, there is no right to counsel in the Constitution, for the same moral reason that there is no right to healthcare: I cannot compel another to act to fulfill my "rights". The word for that is "slavery".