I don't think it's an embarrassment, I think it's just a reflection of the limits of bombing and US power projection. The Houthis survived being bombed by the Saudi's with US & UK support for years. A few more air strikes and cruise missiles were unlikely to stop them.

The US alone has expended hundreds of missiles.

"That includes the firing of 120 SM-2 missiles, 80 SM-6 missiles, 160 rounds from destroyers and cruisers’ five-inch main guns, as well as a combined 20 Evolved Sea Sparrow Missiles (ESSM) and SM-3 missiles."[0] and 135[1] Tomahawk cruise missiles.

Aside from the cost, replacing these munitions will take years.

Barring an actual invasion and occupation of Yemen, it's not clear what the US & allies could realistically expect to achieve.

[0] https://www.twz.com/news-features/navy-just-disclosed-how-ma...

[1] https://www.twz.com/news-features/770-weapons-expended-by-ei...