I have a feeling it has less to do with a foundational nature of evil, and everything to do with a population being impoverished, oppressed, and forgotten.

Instead of trusting your feelings and alluding that the Houthis launch missiles "because they're forgotten", you could list the actual reason they've given, which is enforcing a blockade against ships trading with Israel.

Given that statement, I'm sure that the Houthis will stop their strikes when Israel stops their ongoing genocide. The US could have their shipping lanes back if they stop funding and arming a genocide and force a permanent ceasefire.