"De facto residence" - hardly. Living without papers is dubious and stressful. Trying to build a life when you could be deported is not easy.
"You can’t have nearly open borders and free everything." - don't disagree, free riders are a problem. How many people show up to the US to get their free healthcare and leave, exactly?
"I was a legal resident of France and two of my children were born there and they didn’t get French citizenship, nor even automatic permanent residence."
OK. This is how it ought to be per your views, right? I sympathize for your kids.
Many people do not have family, do not live near their family, do not attend church (for damn good reasons, aside from just not feeling like it. Pretending to have faith so you can have your church friends bail you out is not sound policy).
Your approach won't help the gay former Baptist estranged from their parents.
Even if your motivations are purely selfish, it is worth noting that the US spends more per capita on health care than other countries, so maybe we could learn from them.
https://en.wikipedia.org/wiki/List_of_countries_by_total_hea...
However, public health care spending is ALSO quite here -
https://www.healthsystemtracker.org/chart-collection/health-... (note they provide source data and references)
Ultimately, though, the big problem is that poor people are poor because the system putting them there is a fantastic way to limit freedom in all but name.
If you restrict housing near decent jobs, then most people will, BY DEFINITION, be spending an inordinate amount of money on housing, because all it takes is a few people to say "well I'll push myself and spend 70% of my takehome on rent" before everyone has to do it. This is great if you need compliant workers who fear losing their job.
If you make medical pricing opaque and inconsistent (charging individuals differently from insurance companies) you're telling someone "well you can die or you can just pay whatever we feel like charging you". This is great if you need compliant workers who fear losing their job (and you're willing to offer health insurance). It works even for better-paid jobs too!
Lasik and dentists have price competition, and are pretty affordable, but not critical for life. Hell, even ambulances are losing out to Uber/Lyft (thankfully).
If you make going to college a prerequisite for most decent jobs (18 years of "if you don't go to college you'll be flipping burgers!" in popular media will do that), make it scarce by underfunding it, then offer people draconian loans that can't be repaid by a decent chunk of them, it will be extremely expensive. In fact, the more loans you make available, the more expensive it becomes as people chase it (same goes for mortgages for that matter - increasing funds without increasing supply just raises prices). This is great if you need compliant workers who fear losing their job.
There's a path out of this, even in the US - fortunately folks like Mr. Money Moustache have gained traction as people call bull on the whole system. It involves telling your metaphorical parents their advice is outdated bullshit, among other things, and avoiding the ponzi schemes of housing and student debt.
But don't get sick.