Kuwait and Qatar obtain roughly 90–100% of their drinking water from desalination, Saudi Arabia about 70%, the UAE around 40%, and Oman about 85%. A handful of plants keep key cities alive. For example, the Ras Al-Khair desalination plant in Saudi Arabia alone supplies water to millions of people.
Desalination plants are located near the coast. They’re big. They are hard to defend completely.
If the damage is minor then engineers can quickly repair them. Engineers in the region are highly experienced and skilled. These states usually have water reserves and water can be shipped in, so to really cause severe disruptions the plants need to sustain moderate to heavy damage.
Without water you can expect all kinds of chaos to the region. It would be the fastest and surest way to show Gulf states that aligning themselves with the US is dangerous and that the US cannot protect its allies.
Why hasn’t this been done?
Maybe Iran isn’t able to do it at present. Very likely.
Maybe they don’t want to risk doing it now, because it would enrage so many people and perhaps lead to even worse strikes on Iran. Not impossible, but given how desperate the Iranians are right now they would probably do it if they could pull it off.
The Gulf states, unlike Israel which has a permanent siege mentality, would not be able to deal with a major water crisis and foreigners who settled their to benefit from all kinds of perks the region offered would bolt instantly.
