This isn't a minor nitpick. You've articulating an impossible thing as a target. There is no sane path forward from that starting point.
Fed, housed and clothed is a great baseline, but it has nearly nothing to do with inequality. If everyone in the world was fed, housed and clothed I expect all the inequality measures would be about the same as they are now.
And I think removing the main problem caused by inequality has everything to do with inequality. It's not the end all, but like I said, it's a great baseline.
Inequality of what characteristics?
Because having sufficient food and clean water makes an incredible difference to ones fulfillment and ability to focus on less basic needs.
I'm pretty sure the parent comment to yours was referring to availability of healthcare [and associated aspects such as nutrition and exercise] according to needs, rather than expecting that we can get cancer to agree to a treaty.
But surely it is possible to make them more healthy than they currently are through better housing, through better nutrition, through less stress and uncertainty, through better access to healthcare, through less reliance on "sins" like alcoholism, smoking, and drug addiction because their lives are objectively less awful.
Quit being obtuse.
No, it goes deeper than that. It is impossible for everyone's health to be equal. There is always going to be some very unhealthy people.
Having everyone "fed, housed and clothed" is literally achievable. I can count the people then count the calories, houses & clothes. In practice it wouldn't be perfect, but there is an obvious limit where that baseline can be achieved.
Having everyone "be healthy" is unachievable. In any imaginable scenario within the bounds of current technology and resources there will be a large number of people who we can point to and say "these people aren't healthy and we could do more for them".
This isn't me being obtuse, this is pointing out that "being healthy" is fundamentally a shifting standard changes to be relative to approximating median health outcomes. We can't achieve it as a baseline because as we approach it the baseline will move.
Yes, they might not get the most nutritious or balanced diet but they get the calories they need, oftentimes too many.
This is exactly the kind of moving target the parent is complaining about. Pretty much everyone is fed. But people then move the goalposts and pretend the progress didn't happen because they're not fed nutritiously enough or it requires too much work, etc, etc. I'm not denying that there's more work to do but it's folly to pretend that western nations have not more or less solved hunger compared to the situation even 50yr ago.
You can see this in the statistics for average height, which shot up all through the 1800s. Other countries did not really catch up until after WW2, and then only when they turned to capitalist agriculture.
The evidence that capitalism produces prosperity is overwhelming.
We didn't get government mandated workplace safety until it was basically the norm and people convinced the government to crack down on the places it wasn't the norm.
Many, dare I say most, societal changes follow this "the change mostly happens then the government forces the stragglers to get on board" manner. You simply don't have strong legislation in democracies until after the public opinion has already shifted (see same sex marriage for another example).
Kids make for lousy workers. For example, for the sake of this discussion put aside your moral feelings, and think about kids in your workplace. That's right, there's little useful they could do, and you'd have to dedicate adults to trying to get them to do something useful. Think of what schoolteachers go through trying to get work out of kids. Think of what parents go through trying to get their kids to clean their rooms.
Similarly, child labour is still very common and as far as I'm told in some places even on the rise, so there must be more to the story of its disappearance from the west than "children make bad workers".
That is what made those societies successful anyway: freedom which brought innovation which brought prosperity. Not the fact that they were "western".
If that wasn't true, every employee would be at minimum wage, and Google wouldn't offer free lunches.
The evidence that free markets lift people up is enormous.
Today we have a large group of mistreated sweatshop labourers that produce clothes and gadgets for the industrialized world under conditions that would never be accepted in America, much less Europe. Are those conditions not a result of free markets? Companies who were free to move their production to places that were not encumbered with things like safety laws and minimum wages? And what in the world makes you think that those conditions will become universally a thing of the past without intervention?
No law in Cambodia forces seamstresses to work 16 hour days, no law is forcing the sweatshop owners to demand this of them, everyone involved is in principle free, indeed they are probably freer than I am in my country. That is why the works takes places there and not here.
The labour there creates billions of euros of surplus value that end up as profits for the multinational companies that employ them (directly or indirectly). There is enough money made in the clothing industry to pay decent wages to these people, just like there is enough money in many of the companies in Europe and America that employ the "working poor" to pay people what they need, but it is not done, because by and large companies pay people as little as they can get away with.
This is a problem that can only be solved empowering workers to make demands of their employers. Some workers are rare enough that they have this power by default - I know this, I am one of them, for now. But for the rest, the best way to empower workers is to allow them to band together, either directly in unions, or indirectly via progressive governments making sure that the legislative frameworks that companies operate under result in a decent quality of life, even for those in unskilled jobs.
You can't remove capitalism from the last few centuries of massive progress and just say "it would have happened without it as well".