Most of the rest of the world, as far as I can tell, thinks that the modern state of Israel happened because of the general international reaction to the horrors of the holocaust, as written into international law and things like UN Resolution 181 splitting the British Mandate for Palestine into separate Arab and Jewish states, plus an extraterritorial "Special International Regime" for the city of Jerusalem and its surroundings.

Irregardless of this, if all you consider is realpolitik and see the world through the eyes of just a defence policy, consider that the modern state of Israel is not, despite its impressive military and intelligence services, a completely independent modern power. Consider that it is, by the choices made by its current government, making it difficult for other developed nations to continue to supply weapons or military assistance. For the moment, the strong European defence exporting nations recognise that Iran is a big threat to them, so are begrudgingly still giving military assistance to Israel. But it is begrudgingly, because of their domestic electorate's horror at what is being done to Palestine and the Palestinians.

That leaves the USA. Israel is fortunate that there is a large contingent of Jewish voters in the USA (who, obviously, are very strongly supporters of Israel). The USA will not be a superpower forever. Does China care if Iran gets a nuke? Will China decide that its foreign policy is one of "Great Powers have a sphere of influence, and ours includes Iran", and therefore stop the USA from bombing Iran to slow down the Iranian nuclear program?

These things are why it matters to look good in the eyes of the world.

What "looks good" means is a constantly changing thing as it depends on the personalities of all the other leaders (sometimes it's "look strong", other times it's "speak softly and carry a big stick" etc.), but right now what the government of Israel is doing reduces the support of some the nations it needs support from.

> Also, well, they could instead just be kept in, separated by gender, until they age out of terrorism, as a worse (too expensive), but still acceptable solution.

Kept in what? The rest of that sentence makes it seem like a way to prevent reproduction, which turns this from "Crimes Against Humanity under Article 7(1)(d)" into "Genocide under Article 6(c) and (d)":

  Article 6
  Genocide
  For the purpose of this Statute, “genocide” means any of the following acts committed with intent to destroy, in whole or in part, a national, ethnical, racial or religious group, as such:
  (a) Killing members of the group;
  (b) Causing serious bodily or mental harm to members of the group;
  (c) Deliberately inflicting on the group conditions of life calculated to bring about its physical destruction in whole or in part;
  (d) Imposing measures intended to prevent births within the group;
  (e) Forcibly transferring children of the group to another group.