I agree with the spirit of your message, but you're going way too far using all there. Some are not profitable, and the society is likely better off to socialize these. As a simple example: it's not profitable to provide food and housing for people without means, but if you don't, your society will be worse off - simply because these people will be forced into directions that are generally harmful to your living spaces.
Sure, you could increase police presence in this particular example, but that'd still be an effective socialization, because now you just put them on jail, which is even more costly then just providing them housing and food.
General healthcare is a very ordinary market. You want to go to the doctor once a year to get checked out, they send your blood to a lab to check your cholesterol etc., you pay them money for this. If they find some condition with a known treatment, you pay for the treatment. In case the treatment is very expensive, you buy insurance ahead of time.
The reason people hate it is that people are willing to do anything in order to not die, so they want that level of resources to be available to them, but they don't actually want to pay anything, or to be denied if they decline to pay an extraordinarily large amount, because the alternative is death. But "pay a lot of money or people die" is the nature of it. You can try to paper over it with insurance or taxpayer subsidies but that trade off is inherent and that it makes people uncomfortable doesn't change the fact.