No, not fundamental, only practical.
The EU system of differing national welfare systems, and open borders between member states, is more complex than most people realise, even Europeans. For instance, in the UK access to welfare benefits like a state pension is limited to those with a certain minimum of payments into the national insurance system, which equates I think to around 30 years of full-time work, and gives a certain payment. There is a lower rate for people with some payments. A rate for a top up for a partner of someone with the pension. Those with neither can make a 'voluntary' payment to receive, or are I think expected to work, unless they have specific health conditions preventing that, in which case they can claim other support. EU citizens that moved to the UK had to work a minimum amount, 6 months I think, before being eligible for unemployment benefit. So that's one system, tiered access based on contributions.
Another model is citizen vs non-citizen, with associated 'member' benefits, and operating without consideration of borders (in Ancient Rome it had to be to be relocation to colonies of a certain status, where cituzen obligatiins coukd still be met). The 'cura anonnae' or grain dole of Ancient Rome is an under-recognised early form of welfare, estimated to have gone to as many as 200,000 of the million strong city's poor. In Athens citizenship was by birthright to 'autocthons', those considered to have 'sprung from the ground' there.
A third approach is practiced by various religions. Christian monasticism is probably the best known example in the West, for example with support open to all Christian pilgrims by Hospitalers, the 'original' hospitals. In the UK much of state provision of social care for the elderly and infirm, was inherited from parish church provisions supported by tithes. Sikhism preserves a similar practice with 'dasvand', meaning the donation of the 'tenth part' of each Sikhs income to services at their Gurdwara, which always include food for the poor, some provision of shelter, and basic dentistry and medical care at larger temples. The food hall at the Golden Temple in Amritsar is truly an amazing sight, and they will literally feed anyone and everyone who arrives, regardless of their religion. Islam has strict provisions toward supporting the Islamic community, and not hoarding wealth (early Christianity had these, but dispensed with rules against usury when loans became too crucial to winning wars).
So, to summarise.
A values-based system can provide a basic safety-net to everyone, given a collective commitment to it. I found it distressing to see disabled homeless people living in mounds of rubbish in Fruit Vale just over the Bay from one of the US' biggest richest cities, you have a long way to go this.
A tiered system of access including criteria for citizenship or contribution thresholds, can maintain the sense of fairness required to keep people comfortable with continuing to contribute.
Undoubtedly there is a tension between these approaches, with the first mainly provided by charities and religious organisations. I wonder if the USA not experiencing the very worst impacts of the industrial revolution, or after-affects of mass-participation wars, is part of why the welfare system there is stuck in the mode of the UK in the 1880s. I see it as a tragedy, that people like Bezos feel no moral requirement to provide a tithe toward the community even of his own workers who have become unable to work.
Perhaps the most critical case is mass refugee exodus. These cases can overwhelm what can be provided. Historically, the sources of these movements were often the basis for military intervention & still are occasionally, though increasingly this is seen as neo-colonialism. Climate refugee exoduses, like sparked the war in Syria, are going to be increasingly the norm, as whole areas become unlivable even with charity & government interventions. Currently the safety-net for many refugees is only food and shelter. Lack of effective schooling for refugees has been identified as contributing to a cycle of violence, with lack of opportunities and lack of educated critical thinking among the children who's education was disrupted, leading to more violence & disruption. Finding better solutions to support for refugees, rather than only separating out those rich, well-connected and educated enough to get out of or avoid refugee camps, is going to be a critical factor in reducing human misery in the future. Routes for refugees to access meaningful work, and education to support that, or too often left out.
I would identify this as possibly the most crucial issue facing the world, given the way wars that could start from new tensions will not stay limited to those regions. India is set to lose 50% of it's inter-monsoon irrigation water over the next century, because of lost glaciers. And have already been to war 3 times with their fellow-nuclear power neighbour Pakistan. Increasingly the wellbeing of all, will depend on the wellbeing of every. Practical and moral obligations converge.
