The last Caliphate was the Ottoman Empire. The plan to dissolve it, was published in May 1916:
In May 1916 the governments of the United Kingdom, France and Russia signed the Sykes–Picot Agreement, which defined their proposed spheres of influence and control in Western Asia should the Triple Entente succeed in defeating the Ottoman Empire during World War I. The agreement effectively divided the Arab provinces of the Ottoman Empire outside the Arabian peninsula into areas of future British and French control or influence.
The reason why the Ottoman Empire had to be defeated in battle and then dissolved, is the following:
2 November 1917. Lord Balfour, Prime Minister of the UK. His Majesty’s government view with favour the establishment in Palestine of a national home for the Jewish people, and will use their best endeavours to facilitate the achievement of this object, it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine, or the rights and political status enjoyed by Jews in any other country.
The Caliphate was indeed partitioned by the treaty of Sèvres in 1920.
However, since the civil and religious rights of existing non-Jewish communities in Palestine have been prejudiced, it is understandable that quite a few local populations in the Middle East wish to re-establish the protection from prejudice that they enjoyed under the Caliphate.
The continuing partitioning of the former Caliphate has no particular legitimacy beyond being the historical result of armed conflict, and is therefore entirely predicated on the military capacity of its proponents to prevent the Caliphate’s reconstitution.
In fact, we can generalize this. Legitimacy is never about what you want to achieve or why you want to achieve it, but always about how you want to achieve it. Particular behaviours are simply forbidden, regardless of why exactly you engaged in them. At the very least, you will have to obey to your own laws of war.
In conclusion, the outcome of the conflict about the reconstitution of the Caliphate will entirely depend on the willingness of the belligerents to risk their lives and die for what they believe in. That the best may win.