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.
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.