The answer to "why" is the same as ever. As for the president, his primary concern is "not looking weak" and avoiding accusations of doing nothing in response to the Houthi attacks. Whether or not the actions are militarily useful or merely killing people for little, if any, gain is of no concern (as is the cost to the taxpayer of doing so). So long as campaign money keeps flowing in from those the president seeks to curry favor with, it is "money well spent" as far as a president is concerned. As to why the US armed forces and Navy go along with this, it is also the same as ever -- the mission of the army, navy and air force is to justify their budget. Wasting money like this aligns perfectly with these goals.
People like to over-complicate it, as that's at least not as depressing to contemplate. I did like the simplicity of the commenter who suggested they needed more sacrifices to satan, however. "They are just evil" corresponds well to the "Grug -> Midwit -> Wizard" meme template.