Saudi Arabia is a heavyweight, so why are they getting beaten by the Houthi rebels?

‌I searched on Bullpen and read that the Saudi military has a lot of mercenaries who don't fight with their lives on the line, so their combat effectiveness is weak.
Does Saudi Arabia not have a proper military?
Right now, the Houthi rebels only control the Red Sea strait, but is it possible for them to push all the way in and occupy the Saudi capital?
Looking at the comments on Bullpen, it says that to reach the Saudi capital, most of the route is desert and the residents along the path are hostile toward the Houthis, so there would be heavy resistance. But the US would intervene before that happens, right?