The basic issue I perceive is that you are advocating taking money from one person, by force, and giving it to someone else to pay for their medical care without compensation.
The principle underlying that proposal can only be that we do not have any right to our property if someone else needs it, which they always do. Even if this specific policy does not take away too many rights (by whatever standard you're using), it is based on the principle that we have no rights against the government. "We're taking your stuff because we own you" is not a moral stance.
Your argument implies that all taxation is morally equivalent to theft. If that's true, how do you propose funding public goods like roads, police, or national defense? Does your position hold that all government functions based on taxation are illegitimate?
Do you believe it is morally acceptable for someone to die or face unnecessary suffering simply because they cannot afford care? If not, how should society address these cases without redistribution?
Do you disagree that allowing people to die because they cannot afford care would have a collective impact?
There's a nuance in here, but it's not a bright line by any means.
On the one hand, there are public goods, where all people benefit from them by more or less the same amount. Not exactly the same, but the variance is relatively small. Everyone benefits from roads. Even if one person doesn't drive, they still benefit from the existence of those roads, because they're used for all shipping and transport, to move necessary goods around the country. Sure, there might be a few hidden hermits up in the hills who hunt and grow their own food, who build their own house, and live entirely off the grid... but chances are those hermits also aren't paying taxes, so while they're not benefitting from those roads, they're also not hurt by them.
Many of our tax-funded systems are very similar to roads. It's a collective good, because pretty much everyone who is pitching in for it benefits from it.
On the other hand, there are other programs that are forced charity (for lack of a better term to get my point across). These are programs that only benefit a very few people, but are supported by those who are NOT benefitting from them. Many of these, like school lunch programs, EIT, etc. are acceptable to most people because they're fairly inexpensive to administer. In the grand scheme of things, it's a very small amount being collected from a large number of people, in order to assist a very small number of people. Most of the time, most people are happy to help out someone in need as long as it doesn't hurt them to do so.
Health care is on the gripping hand. It's very, very expensive... but that expense is driven by a relatively small number of people. Speaking as a health actuary with 25 years of experience, it's been demonstrated over and over again that 80% of the cost of health care is generated by 20% of the people; 50% of the cost is generated by 5% of the people. We're not all benefiting more or less the same. But it's also not a small immaterial amount of contribution. Average cost per covered life for employer sponsored coverage is creeping up on $1000 per month. Most people don't incur $1000 of costs in an entire year.
Now the kicker is that most people are already contributing to those health care costs, even if they don't realize it. People purchasing coverage through ACA at least see the actual cost, and they're paying directly (along with subsidies from the government which cover a lot of it). Employees frequently have no idea how much their employer pays on their behalf though, they only ever see their payroll contribution, which can be extremely small. I pay $20 per month for my husband and I... but I also know that the average cost at my employer is over $1000 per person - so my company is paying $920 per person on our behalf every month.
At the end of the day, however, we all have the right to opt out of coverage - we're not forced to participate. That would change if it were universal health care.
Arguments can be made from a premise of morality for either side of this argument. Personally, I don't think morality is the foundation on which this should be built. But that's just me, other people have different perspectives.