When I lived in Houston, my next door neighbor was six months in and out from Jeddah, working for Shell. They actually shipped about half of their product out that way, according to him, aside from it being shorter, Iran has always been a threat that costs them in security if they go out the straits. And again, according to him, Jeddah has always been the contingency plan in the event of a war emergency and it does have the capacity, along with ports to the north and south, to handle just about everything the Saudis produce, along with Kuwait. It's a matter of turning a valve. Not sure that's an option for Bahrain, Qatar or the UAE, but their production isn't that much compared to Saudi Arabia or Kuwait. The problem isn't logistics in an emergency, the problem is that if they do turn that valve, the Saudis and Kuwaitis won't make money off the emergency. The infrastructure investment there, done post WW2, was made by the British and the Netherlands. The Red Sea is the Suez Canal route. You don't go past the Houthi's to the south, you go through the canal to the Med.
The Houthi made some noise, but they do not have the resources to disrupt shipping coming out of the Red Sea. They made some noise, got knocked down, and they can't really get back up.
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