Yes, from a healthcare point of view it makes sense to have the two figures (violent death / others) separated out. But every country combines those numbers, I don't see why the US should get a free pass on that.
And the two do mix, when you get shot in the liquor store but you don't die suddenly healthcare is very much in play, it might even remove that potential violent death from the statistics.
Nobody's looking for a free pass, just an honest view of how long people are going to live. When the numbers are skewed, the resulting debate is skewed.
Along those lines, another well-quoted stat is infant mortality rate, which also drives down life expectancy. But in the U.S., premature babies are routinely saved much earlier than elsewhere in the world. This means that lots of premature babies are more often lost too -- thereby making the infant mortality rates look like something from a third-world country.
You can't manage something unless you measure it, but you can't measure it unless you define it. I'm perfectly happy with a very high infant death-rate and a slightly lower life expectancy rate now that I understand the definitions. But a common understanding is a key component of discussion.
So now every time somebody trots out those same old tired stats we have to have the same conversation over and over again. It's like the old myth that paying money for prevention saves money in the long run -- lots of stats sound reasonable and seem to make a simple point but don't mean what people think they mean.
I think it is mainly a problem of uniform data gathering. Every country has their own methodology, international organzations have theirs but don't do the whole world, just some subset.
None of the numbers are comparable because of all this, it is a big mess. The error bars would have to be drawn so wide as to make any comparison essentially meaningless.
And the two do mix, when you get shot in the liquor store but you don't die suddenly healthcare is very much in play, it might even remove that potential violent death from the statistics.