A good line of questioning, keep digging! Some thoughts from me:

Firstly what even is the welfare state? Where did this concept come from?

My own country of New Zealand was actually one of the world's first "welfare states".

The development of social welfare came from (among many things) the experience of political leaders who fought on the other side of the world in WW1 and came home to find that they had "no jobs" and that life had moved on without them.

What were they supposed to do?

Much had been asked of them by their "country", and the country had an obligation in return. Together with the great depression in the late 1920s the buck stopped with the government, who was forced to take an active role in ensuring there were jobs for people and that certain things were taken care of. In the U.S. this was known as the "New Deal".

This was not just the government being "nice" though. The political logic was that a large number of unemployed military-age men is not good if they decide to riot.

Back in the 19th century and earlier things like war pensions and widow pensions were also key parts of the soldier's life. Who would consider fighting at all, if he was going to be left disabled or with a family who had no source of food?

Thus the historical idea of "welfare" is related with the development of the nation state and specifically the conscription military. Well-paid private armies in small kingdoms are markedly different to conscription forces, and it was exactly the kind of big continental armies that were increasingly required as the nation-state emerged from the 17th century onwards and fought for power.

Arguably, the Western concept of "Nation" really emerged from 1648 onwards with the Peace of Westphalia

Prior to this, people were maybe much more inclined to identify with their local region or district. But throughout the 18th and 19th century the age of empire demanded that these new "nations" create a tribe mentality not just among local communities, but at the larger scale of "countries".

So what about the welfare state today?

Normally no one would expect you to have a "contract" with your child or neighbour in terms of giving and sharing - human decency for our brothers and sisters is engrained into our very psychology since the beginning. But what about someone from the far side of a large "nation"? How do you build allegiance with them?

Nation building required sacrifice and ideological alignment, and perhaps one of the tools was the welfare provided to soldiers and sailors etc.

Today the logic is quite different. There is no universal conscription or military service, and most people are pretty meh about the idea of fighting for their country.

But we still live within the framework of nation-states and this is their logic: taxes are to be paid and public services and welfare are provided.

I do think it is important to be critical of the state and consider other ways, but I think the problem with Libertarian thought is that it requires a huge amount of work to achieve.

Hard-core Libertarianism IS utopian - there is no such thing as a libertarian country today. There is no "blank slate" or desert island where we can start again and try building our free market paradise from scratch. All countries inherit obligations and promises made by previous governments to people.

I don't think it is a question of "how does welfare work in a libertarian state" but "how can a libertarian even state work?"

Fundamentally in a system of nothing but contracts and "private property" and minimal government, is it even possible for a viable economy to emerge? I would argue not. A strong state is always required in the beginning to bootstrap an economy, otherwise it will just get taken over by someone else.

I think the healthy way we should think about libertarianism is as a guide, not a destination: "What if the state was less involved in our lives?", "what if we paid less taxes?"

I believe that prosperity and strong economies do not emerge from "the market" on its own, markets emerge in a kind of dance with a strong and vibrant society.

The question we should really be asking is how do we build strong and resilient societies?

We still live in the world of the nation state. We can imagine new ways of doing things, but we should recognise that is the position we are starting from - there are no more desert islands to claim as our own.

The mechanics of 100% libertarianism require too much in my opinion, and most people will always look for a leader or government to protest when things get too difficult. If that government is not able to "do something about it" then they will be overthrown by someone who will.

Some related conversations on neoliberalism