Maybe not in interest of Saudi gov't but it is in interest of Saudi and Arab people. Regime change in Iran does not mean a strong secular Iran will arise. And a secular Iran poses no threat to Arabs. It's only the regime which uses sectarianism to get others to fight for their interests. I don't think you understand what is going, they are going for you guys next once this Idlib operation is over.^ getting Iran down is not in the best interest of Saudi Arabia. Let the mullah live this way for years to come. If the mullah get overthrown, a new stronger Iran will emerge. A secular Iran is going to be a pain in the ass.
Then Arabs will find themselves under attack by Israel/Iran. The Palestinians and North African Arabs will be under threat of Israel. While the Gulf Arabs/Hejaz region will be under threat of Iran. Now imagine the North African Arabs tried to fight back they have to go through Israel and Iran. I have always judged people by their intentions and ideology. Iranian 'revolution' and ideology is really all about asserting themselves as force over Arabs/Muslims of the region and restoring the great influence they had as Persians back in the day. They realize the two best ways to achieve this are:
1.) Use Islam to your advantage. So they made this twelver Shia sect which requires Shia to adhere to Iranian supreme leader and also this ideology is used to challenge traditional Sunni majority authority over Islam. So they do this by claiming things about the first few Caliphs in order for Muslims to turn to them as authority because otherwise Iran is not required at all to practice Islam. And they realize if they didn't use Islam then they would have to use non-Islamic religion which is not gonna gain them any followers in Muslim majority region.
2.) Pretend to be challenging the US and Israel to win hearts and minds. They realize the people of the region are easily duped by this rhetoric even if this rhetoric leads to them be sanctioned it is worth the tradeoff to them in the long term. They do bunch of this rhetoric to appear as people fighting US influence/Israeli influence and to embarrass Arabs as weaklings who are not independent. All of this is in order to assert themselves as leader in region that everyone needs to answer to.
Arabs are going to be in a worse and worse situation by the day if they do nothing to challenge Iran/Israel. Btw look at my previous tweet of UK foreign secretary, he says a war with Iran is not in the strategic interest of anyone(meaning his allies including Israel/US). And his reason is because it will give opportunities for Sunni militant groups to recover. This shows you Iran, Israel, US, EU, and even sadly some Arab leaders do not want Sunni authority over region to be restored as that is a threat to all their interests.