The Houthi leadership have repeatedly said that they will stop the attacks if the Israeli assault & ethnic cleansing of Palestine ends.
The real naivete is presuming that the "lalala can't hear you, I will do whatever I want" playbook of US/Israeli foreign policy is sustainable in any way.
Lots of people say lots of things. When it comes to geopolitics, actions and capability are what matter. Until someone is willing to underwrite shipping insurance on the Houthis’ word, their leadership’s promises are worthless.