By this logic both Saudi Arabia and Iran should develop nukes just to show the rest of the world…

You are completely missing the point.

Israel developed the nuclear weapon before 1970s believing that it is just a powerful explosive to stop a conventional attack by tanks and soldiers. However, after they developed it, the popular perception of nuclear weapon changed to that of a strategic and political weapon. Now, everyone including you thinks that Israel wanted the nuclear weapon as a strategic and political weapon and doesn’t want to give it up to lose the strategic and political advantage that Israel didn’t plan to create. If Israel give up the nuclear program now, this popular myth will cause citizens around Israel to think that Israel is now politically weaker. Many citizens will start donating to terrorist organization or simply start throwing rocks at Israeli soldiers believing that Israel will start giving up even more. So, Israel can’t give up its nuclear program now without exchanging it to something politically significant.

A simple analogy will be a man and a gun. If a man never had a gun, you don’t think he is weak because he doesn’t have a gun. If a man owned a gun but gave it up, he appears weaker and weak willed even compared to a man who never owned a gun. If a man who never had a gun buys a gun, now he appears stronger than when he didn’t have one. It doesn’t matter if the gun that the man owns is a weak and unwieldy .22 bolt action rifle that he bought for shooting birds that eats from his farmland or a very powerful and deadly Armalite AR-15 that he bought to shoot terrorists. The act of giving up or buying affects how you look at the man and not if he had the gun to start with.

Now, whether Iran or Saudi Arabia develops the nuclear weapon is dependent on if they want it as a political trophy or military weapon. North Korea developed it as a political trophy and sacrificed its conventional army because it only cares about the survival of Kim dynasty. You maybe surprised to know that because South Korea had placed its capital, Seoul within the artillery range of North Korea, North Korea had the option of deploying more cannons and still had the same political effect but chose the nuclear program instead to show it to US. If Iran and Saudi Arabia want it for the same reason, they will get it. They could let the rest of armed force crumble and never bother to develop a complete system for using it that US and Russia have. If they are smarter, they could claim to want it but put in a minimal money for development just for political effect so they can spend money on more urgently needed civilian and military projects.