Saudi is not a monolith.
The single defining picture in US ME policy since 1991 is that in every new crisis the US position is worse than in the crisis before. You're right that the Saudis are not a monolith. The big question is whether the Iranians and Saudis can or will need to reach an agreement. One thing seems certain - their fight is a luxury, existential for neither party.
I disagree with you, a failure to crush the Houthi will be seen as a weakness and encourage the Shia minorities in the region to raise up.