You are seeing states do those things, and presuming (I'm guessing based on where you live) that those actions are therefore the actions of states. They're not, they're the actions of a community.

They're clearly state actions where I live, the organizations they do are politically represented, they get funds from the state budget, they function according to politically voted legislation etc.

The same politicians that vote for them can also reallocate parts of the budget to and from the military, the police force or any other fields.

We do have private initiatives as well, supported directly by the community with money, who govern themselves, who are responsible for every penny they spend, but they're different from the state controlled entities. The legislators generally do not vote dedicated legislation for them, but for the category they fall into (e.g. non-government organization for that matter). You rarely see legislators adopting laws for one specific private entity, if ever when it comes to smaller such entities.

Are you under the impression that the only alternative to "Modern Western State Governments" is "individuals work[ing] by themselves"?

Anything that involves private initiative is individuals working for themselves. If it's not voted by the elected officials, paid from taxpayer money, it's called private initiative - so there is an individual/some individuals deciding the finance and governance and other sensitive issues of the organization themselves.

I hate to break it to you, but states are just very large armed groups, the legitimacy of which is entirely determined by their strength of arms. [...] Israel is a "legitimate" government because they have enough guns (and enough friends with guns) to force others to acknowledge them as such.

That is the way the international system works, of course. But on the other hand, this legitimacy they are provided allows them to worry less about their security and spend their money on the actual social services needed for a state to function. There are, of course, rogue states (yes, you can safely call them that way as well), that choose to terrorize their people instead. But politically motivated violence, whichever side it is coming from, in a country that calls itself the leader of the free and democratic world, does not help in making them less likely to do so. Quite the contrary.