No, your military isn't the reason you don't have free healthcare in the USA. You don't have free healthcare in the USA because of an ongoing concerted effort to prevent it happening by people and companies who make a nice profit from it not happening.

This EP is from 1961, featuring the actor Ronald Reagan, and was played at coffee meetings of "concerned mothers" organised by the wives of American Medical Association members.

https://www.youtube.com/watch?v=AYrlDlrLDSQ

As part of "Operation Coffee Cup".

https://en.wikipedia.org/wiki/Operation_Coffee_Cup

These kind of things are why you don't have free healthcare, anything that provides social good but challenges private profit is immediately labelled socialism by vested interests who have sufficient money to propagate their falsehoods.

It always amazes me what a sufficient plurality of Americans label as socialism that other countries consider to be "a good investment in society".