America somehow spends far more than any other country on healthcare and yet patients still have some of the highest out of pocket costs even when they have expensive private insurance schemes, something is clearly broken to anyone looking and it's not the homeless causing it.
As for why the US spends more than any other country: it's due to an overabundance of caution among the comfortably insured. It's much easier to get a variety of expensive (and often unnecessary) tests and scans (such as MRI scans) in the US. In countries with universal health care these tests and scans are restricted only to those with demonstrable need and they may be subject to long waiting lists.
If it's an HMO, often it's just free entirely. PPO plans tend to have a small fee -- it's never been enough that I've given it a second thought -- and have wide coverage with few limits.
Countries with universal healthcare also tend to have private health companies which can provide tests and scans at a higher speed, either on an insured or a pay-as-you use basis, typically at much lower costs than the US. Yet there doesn't seem to be the same "overabundance of caution" elsewhere. To the extent that precautionary procedures are responsible for high US spend, I don't think that can be decoupled from a system designed to ensure that primary healthcare providers are sales outlets for those procedures.
I mean, it's clear that it's not sustainable to have a healthcare system in which stitches cost this much. Things are not made any better or less outrageous if these costs are transferred to someone else or if they are paid out of pocket.