I personally think it's you missing the point, though I suppose if I were missing the point I might not realise it!
The fact that some healthcare in some EU countries involves profit is irrelevant to my point & the point of the original comment you replied to. Neither of us were saying that the EU is a shining example of profit being out of healthcare (and in fact I was clear to state that the US is not a solo example on that side of things).
The claim we are disagreeing with is that profit = value and therefore lack of profit = lack of value.
Take UK firefighting services as an example. They are publicly owned and funded by taxes, and as such they are not designed to extract profit, just to be funded enough to provide the services needed. Does this mean they have no value? And in a hypothetical world where every country decided to shut down all private fire fighting companies and to fund publicly-owned ones, would that mean there is no value in any firefighting worldwide?
In my experience, people who argue against this model and in favour of for-profit businesses providing these services say that the profit motive leads to better efficiency, competition etc. (which I personally agree with, but that's a separate conversation). I don't think I've ever before seen anyone argue that lack of profit means they have no value.