The relevant change moves from "stop fighting" to "find a way to prevent this vocal minority from controlling policy."

It's not a "vocal" minority. It's a minority that simply engages in violence without regard to what the majority wants. It doesn't matter if the majority of Palestinians want Hamas to stop attacking Israel so they could get a two-state solution, for example. Hamas is going to do it anyway, because no one has the physical ability to stop them. That doesn't change if you inflict more pain on the majority - in fact, it probably gets worse.

If it's a minority of people overriding the will of the majority, the pain on that majority will eventually result in a change. Could be at the ballot box. Could be at the point of a gun or spear or a fist.

Not if the minority has more and better guns than the majority. Dictatorships exist, even if the majority of the people don't want them. Authoritarian regimes exist, even if the majority of the people don't want them. If the minority can kill anyone that opposes them, then there exists no amount of pain imposed on the majority that can change the dynamic. And if the minority doesn't care about pain, not amount of pain imposed on them will change the dynamic either.

This is not just a "pain" issue, and it's not something that will get resolved if the majority just suffers more pain. The framing is simply wrong. You can't solve the problem by having the majority suffer more, and having the majority suffer more will not lead to a positive outcome.

If what you're thinking is that there's a possible justification for discontinuing efforts to mitigate the pain that folks are suffering over there....no, there's not. We can't just walk away from the situation and let it deteriorate into even more chaos and expect that there will be any upside to that.