There is no point in advocating for things that can already exist, this applies to everything and not just "universal healthcare" (which I assume means healthcare paid with taxes by the government); I googled searched the amount of Americans that want universal healthcare and it's around 60%, I don't see 60% of the population funding NGOs (with their own money) that will pay other people's bills for free, hell they won't even organize and create organizations that will make members pay a fee and when someone has a medical issue the bill is paid by the organization if deemed worthy, despite 60% of the population wanting universal healthcare these people won't use any of their resources to pay for other people's medical bills despite this being what they want, this is because they either think the government is a magic organization that can finance any spending with via spontaneous generation of resources, or they want other people to foot the bill, there is a concept in economics called revealed preference which says that what matters is actions and not words, the "universal healthcare" topic and voluntary alternatives to this not existing is a good example of this.
¿Remember how I said at the start that there is no point in advocating for things that can already exist? If 60% of the population wanted they could create a system in which they get "taxed" by a certain amount of money by a NGO they could and would be more than happy to take part, and this NGO would pay for their members healthcare regardless of what it is because it's universal, this doesn't happen because these people don't care, no point in arguing with hypocrites, if you care so much make it happen with your own money.
Let's imagine that these people created an NGO where all members paid a fee to get healthcare, clearly some people could pay more and would want to get more benefits due to this, and some people wouldn't be able to pay as much but still want healthcare, so they would end up paying less and get less benefits, then this NGO would have to deny some claims in order to be able to fund people's healthcare or else it would run out of money, and this NGO would have to hire people to handle legal cases and also hire other administrative personal, they would have to hire people to invest their funds so they have a cash flow instead of a fixed stock of money, they would have to hire people to run actuarial analysis...wait a minute, this almost starts to sound like an insurance company, I guess that if it's an NGO instead of a private company then at least it wouldn't have that huge 6% profit margin that got the CEO of that healthcare company shot by Luigi.