I'm of the strong belief that central management at scale is unilaterally inferior to decentralised and devolved decision-making that can more effectively take local variables into account.
> But for a task of this scale, which has to provide benefits to everyone in the country, I only trust the state with it, and not a private entity.
Trusting the nation state and trusting a private (presumably either commercial or charitable) entity are not the only two options. The charity and taxation options can both occur at a local authority, or a community, level.
It's still state-run in the important sense that the legal mandate comes from the state. This is a major advantage over private initiatives in my opinion. To take a simple example, say there's a legal requirement that people who cannot use their legs are entitled to receive a wheelchair. When that's the law, it means the government (regional, local, whatever applies) has to make it happen, even when it's inconvenient or expensive. When it's a charity or a private initiative, it might not have enough money/incentive/commercial interest/insert reason here to cover everyone.
Admittedly my views on centralized vs. regional governance aren't sophisticated due to my background. I live in a country of 10 million, which isn't too big globally, and I moved here from a very centralized country of 2 million where devolved decision making only makes sense in truly local issues.
Markets are good at preventing this because they separate the requirements (the customers) from the solution (the producers) and provide a Darwinian process to optimise for the best performers, but markets have their own problems and inefficiencies that make them a poor fit (like markets' tendency to ignore customers with unique or rare requirements, meaning people with rare diseases or multiple problems get rejected or priced out by medical markets). There are market-oriented solutions that libertarians propose, such as evening out costs through medical insurance, but markets will always leave cracks people can fall though (such as those who cannot afford insurance, or immigrants with pre-existing health conditions) and introducing state mandates into the market often fundamentally break the market itself (see: US health insurance market). State legislation leaves cracks too when written badly, so neither is a perfect solution in practice. I don't have a solution to these problems because I think they're rooted in patterns of thinking rather than systemic design, but they're interesting to think about.
I was amazed by the concept of free markets when first learning about it, and it seemed like letting market forces play out should result in an optimal situation for consumers, though now I am more cynical and mostly expect bad consequences like monopolists putting effort into not allowing competition.
So due to the different nature of efficiencies and inefficencies of state and private actors, I currently prefer a system where the government is very involved in key areas of human rights, social welfare and basic needs (so education, healthcare, welfare payments, management of physical/mental disabilities, the justice system), and the private sector is mostly handling technical innovation, consumer goods, manufacturing, most services, etc.
Hopefully we've not yet reached the global optimum of these systems and can see both government and markets evolve positively.
I view it somewhat similarly to herd immunity through vaccination. When you have a 95% vaccinated population, diseases can be eliminated. When you have a 50% vaccinated population, it's of course good for those 50%, but doesn't provide the same global benefits.
Is some of the welfare money wasted due to inefficiency? Yes, of course. But for a task of this scale, which has to provide benefits to everyone in the country, I only trust the state with it, and not a private entity.
Can I opt out of the system? No, but freedom isn't a single variable you can straightforwardly optimize for. In this case, I believe the infringement on individual freedom through taxation results in considerably higher total freedom when considering all individuals in the society.