That theory of victory brings an immense amount of risk with it. The Saudis could lose a lot of key infrastructure even in the course of a tactically successful attempt to do what you describe. What you describe is an existential risk to the Houthis, and they would likely respond accordingly. Iran has proven that threatening sufficient destruction of long-lead energy infrastructure can serve to deter military action. The Houthis don’t need to land many or frequent hits to make this extremely costly not just for Saudi, but for any economy directly or indirectly dependent on Red Sea energy trade flows. A lot of the Hormuz dynamics are equally in play here.