The whole ideology of the House of Saud seems to be based around Wahhabi islam, and since the end of the Ottoman Empire the caliphate hasn't been claimed for decades. Why did they never use the opportunity to promote their version of islam by proclaiming themselves caliphs? Did they ever try and fail? Or does it somehow not fit into their agenda?
Anyone can claim the title of Caliph as easily as anyone can claim the title of King of England. It doesn't actually mean anything without recognition. Several people have attempted to claim the title of Caliph in the twentieth century, including the monarchs of the Hedjaz that Ibn Saud deposed. The most recent is Ibrahim, more commonly known as Baghdadi, of ISIS. Both have the same problem as you would of claiming the title of King, without recognition it doesn't mean anything. Ottoman Sultans were Caliph through mastery of the Muslim world, they first claimed the title in 1453 with the conquest of Constantinople but gained it fully upon conquering the previous claimants, the Mamluks. Without recognition of Muslims around the world and with no reputable means of gaining popularity, there is currently no entity that can claim the Caliphate.
Noteworthy is the fact that originally the Caliph had to be of the Prophet's own lineage.