The problem is that the Houthis are effectively irregular Iranian troops. You don't win a war by hunting down every band of irregulars, because that wastes a lot of time and resources for little gain. You win a war by destroying the immobile assets that enable the enemy to supply the irregulars. The Houthis wouldn't be firing Iranian anti-ship missiles if Iranian munitions factories were bombed, but the USA chooses not to do that.

IMO treating any attack by Iranian-made missiles as if it were launched by Iran would be a reasonable policy, but thanks to GWB's Iraq adventure the USA is still too tired from that counterproductive war to vigorously defend its interests in the Middle East. (We did Iran a big favor by overthrowing a strong centralized government in Iraq which was quite hostile to Iran and replacing it with a weak government over which Iran wields a great deal of influence.)