Could this be because US gov healthcare spending takes place mostly via Medicare, which is specifically for people 65+?
Your point is correct, but since the majority of healthcare spending occurs in the last 18 months of life, and the vast majority are on either Medicare or Medicaid during that time of their life (either due to age or ailment-related incapacity), it doesn't make a huge difference.
That means that even though government insurance in the US only covers a relatively small percent of the population, we pay more than other countries that cover the whole population.
I say convert SSA to UBI, set a floor, and let the price of things find a new level with more people in the marketplace: