> But isn't this more or less what I describe still, other than people leaving on their own rather than being forced out?
There's a pretty big difference between people being forced out of their home, and people rejecting a plan given by the UN, then starting a war instead. It's not exactly the same people, which makes this somewhat complicated, but some portion of the Arab-Israeli population left at the urging of those countries on the promise that they would wage war and give them all the land instead of just part of it.
> Like, without going into too tricky political discussions, it seems like being physically present on the land gives you some form of title to it.
Again, some (most? all?) of the land that the Jews settled in between the late 1800s and modern Israel, was purchased or given legally. That gives you title to it, at least in the modern world.
> And if the Palestinians/Arabs hadn't left, it would be much more difficult to run the Israeli state.
Arabs make up 20% of the citizenship of Israel today. And yes, this is "problematic".
There's a large question about what sovereignity means in this kind of context. Does it make sense to have a "Jewish" state? How can that be democratic? You can't restrict existing citizens, even if they are non-Jewish, but then how do you maintain it as a homeland for Jews? These are tough questions that I don't think anyone can really answer.
> If so, I don't see what it has to do with corruption, because it's just a basic fact of countries - one guy has to win and the other one thus loses, and it's a zero-sum game.
Many things in life are not zero-sum. But yes, if two different ethnic groups want the same piece of land, and feel they are entitled to it, one of them is going to "lose" in that sense.
> What's the way out of this conundrum?
There isn't really a good way out, not without the Palestinians making in their eyes major concessions. (Though note that Israel has attempted to make plans that made major concessions from their pov, and the Palestinians rejected all these offers.)
The only solution I personally think makes any sense is a two-state solution, whereby the Palestinians get their own state on the existing land, plus possibly some part of Jerusalem (though this is a political non-starter today in Israel.)
But I don't really see this happening. Palestinians don't love this deal (for obvious reasons.) Israel, on the other hand, is the stronger party which means it probably benefits from the existing status-quo, so has no reason to rock the boat right now. And for leaders on both sides, it's possibly better to keep the fighting going.
So really, I don't see anyone with any big incentive to change any of the current situation.