Exporting oil from the west side of Saudi Arabia works until some armed group like the Houthis with drones/missiles places a credible enough threat at another chokepoint that the ships won't go.
The choices are then to find a way to get the Houthis to chill out, or use enough military force to cut off the Iranian support for the houthis, or use military force to be confident you have destroyed the houthis' ship attacking capability.