If Iran goes nuclear, it will act as an umbrella that will help assure the regime's immediate security like North Korea. Unlike North Korea, Iran is actively trying to spread its influence across the Middle East, and nukes make Iran itself hard if not impossible to respond to militarily. Nobody has ever attempted to invade a nuclear power.
North Korea is not being invaded and wasnt invaded since 1950 because it has an enormous conventional weapons arsenal that will kill several million people in Seoul if there is a large scale war. Nukes have nothing to do with North Koreas security.
Iran similarly is not in immediate danger of being invaded. It is an incredibly well defended country, especially post 1980. Its immediate neighbors who used to pose threats have been eliminated (Taliban and Saddam). It has gained allies in the region (Hezbollah, Syria, Iraq, Afghanistan, Hamas). It has a large population, very good terrain for defense, a very strong sense of nationalism in the population, a fairly developed economy, etc. Invading Iran would make the Iraq war look like child's play. There is simply no chance of an invasion of Iran by the USA. Iran is already doing what it wants to do in the region and there is no invasion of Iran. There is nothing Iran wants to do that it cant do right now because it doesn't have a nuke.
A nuclear Iran will spark a Middle Eastern arms race. Saudi Arabia will nuke up next via Pakistan, Egypt and Turkey will be likely to follow. This makes for a much much more unstable and dangerous Middle East, and will likely force Israel to take more proactive measures, like building ICBMs or SLBMs, or strikes against nuclear facilities. This is in almost nobody's rational best interest, but it will happen nonetheless.
I dont buy this. Saudi Arabia percieves no threat from an Iranian nuke. Nobody thinks that Iran would commit suicide in order to land a nuke on a neighbor's city. This idea is just not even considered in the American and Israeli intelligence establishment. Its an idea that only exists on the internet and among right wing fear mongering politicians.
Saudi Arabia has the world's super power backing it. So does Egypt. Turkey is in NATO. And even if they weren't, Iran has never shown even a slight interest in invading them. Its a well defined nation state that is not interested in expansionism or conquest. And if for some reason Saudi Arabia decides to purchase a nuclear device, I fail to see the danger from that. Egypt and Turkey see no threat from either SA or Iran. If they want a nuke it will be for other reasons other than insecurity. The proliferation argument simply fails.
People point to the fact that 4 Arab capitals have come under the control of iran as an example of Iranian expansionism but thats BS. 1) Damascus chose to become allies with Tehran in 1979, not the other way around. Iran is in no way responsible for Damascus becoming allies with Iran. All Iran is doing is giving aid to Syria to prevent it from being dismembered. This isnt expansionism. 2) Sanaa fell to Houthi rebels who have almost no connection to Iran. They are the same religion but thats it. Arab Shiites can do things without having to be under the influence of Iran. 3) Baghdad was converted to a Shia capital by the USA, not Iran. 4) Beirut is not controlled by Iran, it is supporting the Shia minority's political organization, Hezbollah, but they arent controlling the government or attempting to do so.