As I wrote before and initially, a political solution is the most realistic option long-term.
KSA nor any other outside power is interested or willing to potentially sacrifice (worst case scenario) 1000's if not 10.000's of soldiers to root the Houthi terrorist cult out completely from the territory of Yemen that they control.
The Houthi terrorist cult, due to Yemeni state failures (Yemen as a political entity has been one big failure since the unification in 1990 despite being blessed with amble fertile lands, some of the world's most strategic sea trade routes, a large succesful diaspora, large population, one of the world's oldest civilizations and cultures etc) but due to internal Yemeni failures, the status quo is as it is.
The Houthi terrorist cultists would never have succeeded to this degree if the Yemeni state was strong and Yemenis were united.
99.99% of the brunt of the Houthi terrorist cult evils befalls Yemeni people themselves (mostly those that are unfortunate to live under their incompetent rule) not Saudi Arabians or other Arabs or Muslims.
As demonstrated recently, Houthi terrorist cult attacks on KSA is only a disruption - not an existential threat.
My hope is that the Yemeni people will eventually rise up and become tired of living in absolute misery (under Houthi terrorist cult rule) and that the Houthis themselves will eventually reform and realize that they need to live in peace with their main and most important neighbor (KSA) that they border directly (2000 km) if they want prosperity and stability and that parroting the Iranian policy in the region is a death sentence long-term.
Once again the problem was never the Zaydis - who until the Houthi coup in 2014 remained the dominant military and political force despite being a minority in Yemen (35-40% are Zaydis rest are mostly Sunni Shafi's). Ali Abdullah Saleh was a Zaydi himself. KSA was the main ally of Yemen back then as well.
I already covered the relations pre-1970 when North Yemen was ruled by the Zaydi Imam/King. Same story.
On the other hand you would like to see the menace,for the sake of Yemen, Yemenis and region to be dealt with harshly and swiftly, even if it would cost a lot, but there is always the fear (in the context of Yemen) that 5-10 years down the line (even without the Houthis) the Yemenis will start another civil war. Or turn on KSA or their allies.
Unfortunately with Yemen being the most tribal Arab state and most complex in this regard, tribal loyalties can change very quickly and many tribal sheikhs and leaders are very opportunistic.
The idea that somehow KSA (regime, people or just general common sense) are interested in an unstable southern neighbor that we share 2000 km of borders with and almost everything else (people to people ties, cultural, historical, ancestral, linguistic, religious, geographic) is pure lunacy. Nothing would benefit KSA more than a stable and prosperous Yemen and wider region.
Even more so when KSA has been focused on internal and regional growth.
As far as Iran goes, I am 100% sure that the moment the current Iranian regime is toppled or truly reformed, KSA and Iran will have cordial ties like before 1979. Or even during large parts of the 1990's under Khatami.
But it is hard to argue with religious fanatics and their religious propaganda that they cleverly use to fool the average Ali and Muhammad within their own borders and outside of it. Of course the Houthi terrorist cult does not even belief (leadership) 1% of the propaganda that they spew against their own people (Yemenis), KSA or others.
Quite frankly, the region should take a look at how Europe reformed after WW2 and stopped killing each other 24/7. Even though the Ukrainians and Russians have not read the memo this time around or the Balkans before but nevertheless, you don't see the Brits or French killing each other anymore or the Danes and Swedes or the Germans and French etc.