Oh, you're deferring to intensely made up nonsense from over a decade ago. Honestly, I didn't think you could have a worse source than anonymous tweeting, but you may have found it.
For anyone curious how they reach their number, they took the counted stat for public school students (rather than the overall government estimates, can't trust those), and multiplied that by another statistic from a different source for age groups of homelessness claiming 51% of homeless children are younger than 5 and would not be counted. Mind you, their definition of homelessness is so broad as to include "living in doubled-up situations", so if two families share a house like a young mother has a roommate or siblings choose to live together or many other completely reasonable things that people do, that qualifies as your child being homeless. Like, for this living in a hotel is homelessness, so if a millionaire's home is destroyed in a flood and his family lives in a hotel until they can find somewhere new, that's homelessness. All of this coincidentally leads to the highest possible estimate they could make, and oh yeah, their organizations purpose is to create the data to drive government actions, what a crazy coincidence that they have the most extreme conclusions...
I think, ideally, every human being should be capable of earning enough from an honest job to pay for necessities for themselves and a reasonable number of dependents, save money for old age, and afford a reasonable amount of luxuries. Capitalism is clearly not providing that for a large percentage of the population.
And in the event they can't provide for themselves, then society steps in to assist for necessities, and even a small number of luxuries. This varies, but it's not hard to see that there are frequently substantial shortcomings in societal support systems in many countries.
And I would argue here that in many cases the increase in welfare reflects the fact that in the last 40-50 years capitalism in many countries has actually become worse at providing good jobs for our countries. Taking a quick look at a graph for median earnings in the USA is an example, or likewise increases in wealth inequality in many countries. The government has therefore increasingly needed to subsidise workers to make up for their inability to earn via work.
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If what we're talking about as satisfactory is people not going homeless or hungry, that's the limit of our societal ambitions, then yes the system is a failure.
I would say that talking about much more than keeping people fed and housed very quickly approaches contradiction.
It is interesting that you say the ideal is for people to earn enough to provide for themselves. I would agree, I'm sure many here would not, many would question the necessity of earning that, especially since the earning is implied to be specifically money. We have to ask the question of what the distinction is between earning the money to spend to have necessities and some luxury for oneself and dependents versus just having those things provided. Obviously on a societal scale, there is the practical difference that the things you do to earn the money are nearly all directly providing those necessities or luxuries for someone else, but setting that aside, what is the distinction between earning a living and having things provided to you on a personal level. I think the difference lies in power and agency, where what we get is a result of our own decisions. If we look at the difference between food banks and food stamps, the latter is often preferred by people, and I think that's because it lets them have what they want on their own terms. People would classify that as having more dignity, I would personally say the grace to accept the charity of others is probably actually more dignified, so I think the desire for agency is really where it's at.
Which is where the contradiction comes in, if the ideal is not just to give people what the need but rather to empower them, to have them build their own life through their own efforts, there is inevitably a line at which government intervention takes more agency from people than it is giving back. Enabling people to more easily acquires homes I would say empowers people, but making a world where it is impossible to ever be lacking would involve taking all power and agency away and giving it to the government. What to do next for any given policy requires an honest assessment of what side of that line we're on.