From what I understand, and I could be very wrong, the fear is that directly attacking the Houthis will be seen as an escalation by Iran. The west doesn't want to get mired in yet another war in the Middle East, so instead they've adopted a defensive posture around their shipping lanes with Prosperity Guardian. This is also why Saudi Arabia's own navy vessels are conspicuously absent from the operation, despite the Houthis being a geographically prominent thorn in their side.
> fear is that directly attacking the Houthis will be seen as an escalation by Iran
It would, but that’s not really a constraint. Iran is in no position to risk direct strikes on its territory. It’s more simply that nobody wants to get bogged down in Yemen. So there is an element of hoping someone else will start bombing or Tehran getting their proxies under control.
Yes, and it was a disaster. The Houthis could aim their missiles at Saudi oil infrastructure again. Much simpler to let America handle both finding a solution and taking the fire.
Those are the same conflict though. The saudis are fighting the Houthi’s in the Yemeni civil war. The same group that’s attacking the ships in the Red Sea.