Israel isn’t directly threatened by Iran having nuclear weapons either unless the leaders are willing to give up their lives and country for their goal.
The problem with populist-leveraging theocracies with bad economies is that you need a shared national boogie man. For decades, Iraq, Israel, and the US have been that for Iran.
Well, you need the boogie man if you're the dog and your goal is to keep your country under control.
But if the tail gets ideas about wagging you? And your populace demands you eliminate the boogie man threat with all means at hand, because you've spent decades inculcating hatred in them and blaming ills on the man?
Well... better the boogie man's head than yours on the chopping block.