Yemen is a mess with a UN seat and always has been. But that does not mean Saudi Arabia's alliance isn't making progress:
The UN is accusing the Shia rebels of deliberately blocking delivery of food aid to areas that face starvation without it. This is being used to persuade the UN to apply more pressure on the government and the Arab Coalition forces to halt their attacks on the rebels. The Shia rebels are growing desperate because their military and economic situation has gotten much worse in 2018. Since the beginning of the year the Shia rebels have suffered from a sustained and widespread cash shortage and have been unable to pay many of the government employees in Sanaa. Because of that the loyalty of these unpaid (some since late 2017) civil servants is suspect and the rebels appear to be losing control of the capital. Over the last few months there have been more public protests against the rebels in the capital and that has led to arrests and beatings. ...
The [Yemen] government offensive against the [Iran-backed] rebels has been moving into more rebel territory all year and as rebel controlled territory shrinks rebel morale plummets. The Arab coalition sees victory as inevitable because the rebels are not only growing weaker but Iran, their only foreign supporter is also less able to get support (especially weapons and cash) to the rebels.
Yemen itself will still be a mess after the rebels are defeated. The separatist Sunni tribes down south still want to partition Yemen into two nations. AQAP has good relations (often family or tribal) with these tribes and continues to find sanctuary in these tribal areas.
So the Saudi-backed coalition is making military progress as the rebels weaken.
The humanitarian crisis is being engineered by the rebels to get the UN to save them against Saudi military success.
If we look at the war casualties, we see that Yemen is hardly the unprecedented slaughterhouse that Iran-friendly propaganda would have us believe it is.
In Yemen, the casualty toll ranges from a low of 10,000--which is clearly too low given that number has remained static for a while--to 50,000, which could be too high given how the tendency to over-estimate deaths to get attention is done. Let's say 30,000 as a very imprecise compromise. That is over 3.5 years of fighting and represents about 8,600 dead per year.
Compare that to Yemen's civil war in the 1960s, where 100,000 to 300,000 died in 8 years and 2 months of war. Using the same imprecise compromise, that is 18,400 dead per year.
Or Ukraine where 10,500 have died in 4.5 years of Russia's invasion of the Donbas region. So over 2,300 dead per year can be basically shrugged off there while 8,600 is a number that must generate outrage?
Where are the dividing lines? Because the Syrian civil war of 440,000 (again, an imprecise compromise) in 7.6 years of war gives us 58,000 dead per year, which the international community is apparently okey dokey with in its refusal to stop it.
Do we not care up to a 2,500 rate because it is "low" and not care because 58,000 rate seems too hard to tackle--and 8,600 is in the sweet spot of practical concern?
Further, when an enemy uses human shields--as the Houthi do--they are responsible for the civilian casualties that result and not the people dropping the bombs on what are believed to be military targets.
And finally, even when the war is over it will still be a mess and likely just a pause as factions reform with new alliances and renew the struggle in some form in the future.
And we will still have the job of hunting down the al Qaeda and related jihadis who have made Yemen a sanctuary. Do remember that President Obama actually called our fight there "the model" theater in our war on terror.
But hopefully that will be without Iranian influence that could give Iran a position in the Horn of Africa to interfere with oil shipments from Arab Gulf states that bypass the Strait of Hormuz which is under the Iranian gun. Iran's shipment of missiles to bombard Saudi Arabia and hit Saudi alliance warships could be shifted to oil ports and oil tankers.
The complaints about the Saudi-led war run afoul of our efforts to leverage friendly forces without committing our infantry--remember that Yemen was once the praised "leading from behind" model for Iraq War 2.0--and sound too much like Iranian propaganda. We should not go along with it.
Not that I dismiss deaths in the war. The level is bad whether it is at the Ukraine rate, the Syria rate, or the Yemen rate. We should help with humanitarian aid despite Houthi interference. And we should help the Saudi coalition avoid inflicting civilian casualties. But the bulk of responsibility for deaths is not mostly on our (for the moment) side.
And given the history of Yemen, fighting will continue regardless of what any outsiders do, and we should at least try to keep Iran from winning this civil war.