While poverty is a condition which the state contributes toward, by upholding social orders that keep socioeconomic losers as losers, that does not mean that welfare is not a benefit. Welfare is an attempt at balance without massive social change.
I've been listening to a lot of Jonathan Haidt and Jordan Peterson and I think they both have elaborated some important insights. (btw it would be unfair of you to dismiss me based on any prejudice you may have regarding these men, JP especially is polarising I know). One key insight is that of conservatism, that changing society radically is potentially dangerous because we can't predict the results. Thus we have the gravitation towards norms, and the enforcement of these norms, and a resistance to changing them. Haidt's contribution here is that openness to new experiences and other personality traits largely predict political orientation, and so those willing to make changes often make their judgements based on emotion and partial .
5 years ago I would have said that because poverty is a necessary effect of the systems we have in place that we need to remove or radically change them. Stephen Pinker recently came out with a book Enlightenment Now in which he makes the case that things are actually getting better over all. That goes for poverty too. Now I haven't actually read the book, I'm hoping to get it as an audio book, but I've seen data that supports that before, perhaps you have come across some similar information.
It's true that the state maintains poverty even in fundamental ways, such as defining private property. It's not clear that government programmes such as welfare work to alleviate it (there's evidence it makes it worse in some cases) though the case of my own country (Ireland) it's more surely indicated that it does work, at least for most. However as we've seen historically removing private property has not worked in practice. There are some middle ways which are interesting, collective ownership, co-ops, etc. but I have observed that these things are practically limited.
The other claims of benefit I think are easier to see and I don't think you can dismiss them by making the argument that the benefit is relative to income / wealth / class. For example, the lower class person who gets a lot of utility from universal healthcare doesn't get a lot from access to markets, as they work in a factory. The middle class business owner who has private medical insurance gets access to markets, ability to incorporate their company, business tax breaks, etc.
Protection abroad is real. I doesn't mean Navy Seals are going to jump out of the sky to save you from getting mugged, but your country will go as far as trying to bargain with terrorists for your life in the extreme case, or just embassy access which can go a long way, depending on your country.
The other point you make is that the state is not required for much of this. I agree, but that's quite hypothetical. We find ourselves now in a world of states, so it's neither here nor there whether these things can be provided / required without states.