Yemen is of no consequence in the region. Their only natural resource it, is "Strategic location". It's political system is "Civil War". Yes, battle hardened, due to decades of civil war. And that is amongst several different warring parties. Sort of like, a poor man's Afghanistan (without the Taliban). By far, the least developed, lowest income economy in the Middle East. Their economy based on agriculture (in the middle of a desert) and fishing. NO OIL, not worth a second look by the US. There is no sense in "bombing them into the stone age", they are already there. Their one and only support is Iran. Iran sends them some missiles, directs them to blast any ships going by.
Plus, Saudi Arabia, is viewed as US's lap dog. definitely not a major force in the Middle East. This was proven during Iraq's march into Kuwait, as Saudi's watched, panicked and summoned US / Desert Shield. You really think US was concerned with WMD, helping Iraqis, or Saudi Oil and money?
US foreign policy in the Middle East, runs on a single principal, how cheap can we extract the oil, and how much weapons can they afford to purchase. All US motivations are so clear, yet so subterfuge.