"sheltered homelessness" is an important metric, but it's not the one I would to differentiate between levels of income/wealth redistribution, precisely because it affects such a small part of the population.
the metric(s) I would use need to be ones that are meaningful (and meaningfully different) for more substantial parts of the population.
So, some suggestions could be:
* medical care induced bankruptcy
* personal bankruptcy in general
* percentage of income spent on housing costs
* disposable income after housing, health care, education and transportation costs
* some measure of "timely" access to medical care
* inter-generational economic mobility
There are certainly issues within the EU with any and all of these (worse in some places than in others), but overall my understanding is that the US generally does worse on all of them.
I am originally from the UK, and I would argue that while there are aspects of quality of life here in the USA that are vastly better than the UK or the EU, most of those things are primarily the domain of those who make median or above median income. I certainly don't think that the economic system in the USA is better than those found in the EU, even though there are some metrics where you might make that case. But mostly what the USA has a lot of that the EU has much less of is economic churn - businesses constantly starting and almost all of them failing, followed by more businesses starting etc. This gives the impression of very prosperous, active economy, but I would question whether we really do much better out of this model than the EU does with their much less entrepeneurial systems.
> if you go too far with redistribution you remove the incentive for people to do difficult or unpleasant work
The people who earn the most in our system are not the people who do difficult or unpleasant work, and it just seems preposterous to me to suggest that there is a link here.
> In a less extreme example we just witnessed France default on its pension obligations!
This is not an example of what I think you're claiming it is an example of. Defaulting on pension obligations is about a failure to honor past labor contracts, not income/wealth redistribution.
> How can we honestly consider expanding wealth distribution programs when we can’t even afford what we have now?
Same way we can afford a war whenever "we decide" to fight one. Same way we can "choose" to spend more than the next 10 top military spenders combined. We are a rich country, and we could choose to place substantially more emphasis on the quality of life of all our people. But we "choose" to do otherwise.