Saudi Arabia has not asked Pakistan for anything. In fact, It was Pakistan that expressed interest to join the collation and when asked to it backed off. The GCC was not only able to take a collective measure to kick Iran out of Yemen but also pulled out a UN resolution 2216 that justifies its military operation. So far, the collation was able to librate 85% of Yemen territories that were under Houthi control. The Saudi Army has worked impressively to keep the border safe and execute missions inside Yemen itself. The Saudi Arabia along with the navy announced Yemen space and maritime restricted in a matter of 15 min. It has also worked impressively against Al-Qaeda and the operations are still ongoing. This is not an adventure rather the need of the hour thing to do. Saudis have the logistic and financial means to sustain all scenarios. They are not only spending on the operations in Yemen but also the world largest donor to all affected countries around the globe. Its true that there were some errors that claimed the lives on a few civilians but that is made sure not to be repeated. This is a war after all so causalities is expected. Iran wanted to create mini Hizbollah in Yemen but that is a red to the Saudis. Not on their backyard. Sorry if I miss any of the raised points.
Pakistan:
Pakistan is in the habit of 'volunteering' its forces for specific operations with the end goal being that some compensation is had by Islamabad. This is well understood by the UN, Saudi, and everyone else. I don't think there's anything wrong with this arrangement. After all, soldiers must eat too, but to say that Pakistan unilaterally volunteered for service and then withdrew when Riyadh placed religious restrictions (Sunnis only) on whatever force Islamabad could provide seems incorrect. Even in that event, Saudi Arabia's preconditions created a rupture in a long-standing agreement between the two countries and diplomatic efforts to salve this are ongoing.
Saudi Arabia is forever (and rightly) wary of Pakistan's relationships with Iran. The Pakistani Army is not the Saudi National Guard. It really does have soldiers from all over Pakistan in it and trying to divide it along confessional lines was a massive misstep. Rawalpindi took great relish in rejecting the notion of a Sunni only force and the GoP and Army got a lot of good public relations out of it.
UNSC Resolution 2216:
On this I concede the point that Saudi Arabia has largely been able to line up Western diplomatic attitudes against the Houthi rebels. This should not come as a surprise however. The Houthi, of course, do not have representation at the UN, and as we can see most famously from the vote to authorize the Korean War, it really does matter who has a seat at the UNSC.
What I think is more important is how little the West has done to help Saudi Arabia out in their mission. If D.C., London, Paris, etc. saw Yemen as a top priority to their interests or even as an easy win against ISIS or AQAP, they would have committed more fully. A better measure of Saudi's diplomatic prowess would have been to create a wider meta-coalition that more fully supported the Islamic coalition on the ground in Yemen.
In short, Saudi Arabia was able to paint a rebel force that looks an awful lot like ISIS to a CNN camera that enjoys its "Death to America" chants as much as anyone as the 'bad guys'. Congratulations, I guess.
The Situation in Yemen itself:
You are correct that Saudi Arabia and its partners have been able to liberate a lot of Yemen's total surface area, but not the parts of Yemen that the Houthi are determined to hold on to. The Revolutionary Council still controls what it needs to control to continue to the fight, namely its homelands and much of Sana'a. You are correct that Saudi Arabia and Egypt were able to establish full maritime dominance over Yemen's waters, but again, the Houthi have no navy. This is not an accomplishment. A similar situation applies to Yemen's airspace.
On the humanitarian front, there are wider issues than the accidental killing of civilians. Shortages of food, water, and medicine will continue to grow and exacerbate the underlying issues of the conflict. I'm not blaming Saudi Arabia for this, all of these things are natural results of war and unrest. I am saying that the longer this conflict persists, the harder it will be for Saudi Arabia to build Yemen back up to a state considered acceptable by the international community. If Saudi leaves Yemen after 'accomplishing their mission' in a very weak state, there will be little to no prophylaxis against a new terrorist or insurgent offensive.
I do not wish to insult Saudi Arabia. Their military was asked to do an impossible thing. Saudi Arabia's mission in Yemen, on a strategic level is three-fold: secure the border, tie the GCC closer together, and contain Iranian influence. My contention is that on the first goal, this has been a success. On the second, it has been a wash. On the third, while Saudi Arabia is distracted in Yemen and Syria, Iran is able to operate with a free hand everywhere else. The resources that Iran has to commit to keep the Houthi going are a pale fraction of what Saudi Arabia has to commit to counter Iranian influence. This is the dictionary definition of “bleeding someone white”.
I maintain that it is in fact impossible to fully defeat the Houthi rebels or AQAP/ISIS insurgents in Yemen. Saudi Arabia simply does not have the power or money to impose its will on Yemen indefinitely any more than the United States was able to in Iraq. The only solution is a political solution, and this will have to include Iran and the Houthi.
The problem is that I don't see any move that Saudi Arabia is making to support a political solution. What about the Oman plan? What is an exit strategy that solidifies Saudi's securing of its border and simultaneously weakening its regional arch-rival? That is why I don't understand Riyadh's strategic goals.