When people say the US doesn't have universal healthcare because of the military, they usually mean there's some relationship between the enormous amount of money spent on war and the cost of healthcare. But single-payer healthcare is less expensive than privatized healthcare, both in expense to the state, and the general cost out of pocket per citizen. I think there is a relationship though.

Universal healthcare means healthcare for all races. The military is constantly going to war against racialized enemies - Germans, Japanese, Koreans, Vietnamese, Iraqi and Afghan Arabs. Dehumanizing them is a feature of war propaganda. This makes the armed forces a bastion of white supremacy, and as documented here is constantly injecting violent white nationalists back into society, who organize to re-enforce white supremacy in civilian life.

I don't think white supremacist political resistance to universal healthcare is the only reason the United States doesn't have it, but I think it is one of the factors. I think it is also a factor in school shootings, toxic gun culture, and hyper-violent police.