Great points but sometimes rebellions are also crushed decisively. For every CCP or Taliban victory due to advanced arms being stolen, we could discuss countless cases from the last hundred years of crushing defeats despite the acquisition of such arms.
The "will to win" is questionable for the Americans in both the cases you have cited. One could argue that they simply cut their losses (substantial as they were) on far flung battlefields and fled back home many 1000s of miles away. Alexander the Great was no different millenia earlier. Logistics played as great a role here as did anything else.
KSA is not some far flung realm. It borders Yemen. Iran is, of course, also geographically somewhat close to Yemen but Iran now has its own problems. Iran already can no longer support Hamas and Hezbollah in any meaningful ways - granted they are further away than Yemen is. I'm not so sure that the MDA signatories are the ones who will struggle to support the necessary logistics channels in this context.
Let me first answer your initial question. Modern military logistics—or logistics systems in general—exhibit a counterintuitive phenomenon: distance is not the primary factor determining cost.
For instance:
Shipping a batch of supplies from Chengdu, China, to Karachi costs significantly more than shipping the same cargo from Shanghai. The fundamental reason for this is that maritime transport is far less expensive than land transport. Even within China, the cost of transporting large quantities of coal from Xinjiang to cities on the southeastern coast is higher than the cost of shipping it there from the United States.
Admittedly, there are differences in transit times. However, when weighing transit time against economic cost, people generally prefer maritime transport.
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With Saudi assistance, the Yemeni government forces possess a weaponry system far superior to that of the Houthi rebels. Yet, they have suffered widespread routs. This clearly demonstrates serious internal organizational and management deficiencies within their ranks. If the Saudi-led coalition continues to support them in this manner, the result will simply be a further strengthening of the Houthis.
This has fully proven the utter failure of Saudi Arabia's "proxy war" strategy. Should Pakistan and Turkey intervene, it would only further confirm Saudi Arabia's complete incompetence. ------Saudi Arabia initiated a proxy war, yet neither its proxies nor the kingdom itself could secure a victory; now, it is forced to beg its allies to join the fray. This is an act of sheer cowardice.
However, even if Pakistan and Turkey were to intervene militarily, could Saudi Arabia—or the Saudi-backed Yemeni government forces—actually win this war?
There is absolutely no chance of that!
Undoubtedly, a direct military intervention by Pakistan and Turkey would deal a heavy blow to the Houthis. But who would carry out the final phase of the war: clearing the battlefield and securing the territory? That is a critically dangerous undertaking. ------ Turkey and Pakistan doing this job? Only if they had lost their minds. Saudi Arabia lacks the capability. The Saudi-backed Yemeni government forces are even less capable.
After some time passes, the Houthis will continue...
Who wins?
Here is another point to consider.
At their core, no human being wishes to be controlled or swayed by others. Any acceptance of external control or influence is merely a temporary measure driven by the instinct for survival; the moment individuals gain the capacity to stand on their own, their first move is to shake off that external control.
Countless events throughout the history of human civilization have amply demonstrated this truth—one need only look back at similar historical precedents.
Therefore, should the Yemeni government forces decisively defeat the Houthis and secure full control over Yemen, their first move would be to break free from Saudi influence. By the same token, if the Houthis were to ultimately triumph and gain total control of the country, their first move would be to break free from Iran.
Does Pakistan really want to get involved in this game?