While I am not Muslim, it is my understanding that it is considered sacrilege and sinful to lay siege to Mecca and Medina in Islam, so it would only be a justifiable action if viewed as reclaiming the two holy cities from an illegitimate ruler. While the Saudis did consider the Ottoman Sultanate's claim to the Caliphate to be illegitimate, I have read that their reasoning was that they did not control the two holy cities (since the Saudis themselves had conquered them). In my admittedly limited understanding, only the Khawarij considered this might-makes-right approach to claiming the title of Caliph to be a legitimate means of arbitration.
Indeed, I am not aware of any time in history between the death of Muhammad and the Saudi conquest of Hejaz in 1803 that Mecca was not, at least nominally, held by a political entity claiming the Caliphate (or ceremonially through vassals), unless the brief Qarmation interlude is included. For a ruler that did not claim the title of Caliph to besiege and capture the cities of Mecca and Medina was therefore a significant break in nearly twelve centuries of Islamic tradition. Given that the Saudis expounded (and at least theoretically, continue to expound) a pan-Islamic Wahhabist doctrine, why did they not attempt to proclaim themselves Caliphs, and how did they justify their capture of Mecca without being Caliphs?
We had a discussion about this a few months ago here: Is there a reason the Kingdom of Saudi Arabia has never claimed to be a caliphate?. You might find the discussion there interesting or at least a partial answer to the question.
For whatever reason, the al-Saud just never appeared that interested in the title. Perhaps they considered it an innovation (bida') which, in Wahhabi doctrine is considered undesirable (this is a total guess on my part). Wahhabi doctrine stresses the importance of God and Qur'an and pretty much nothing else--even now, the king is custodian of the two holy mosques, but has never pretended to have any sort of religious authority the way that the caliph did (neither does the chief mufti of the kingdom).
I will say on the second point that, while control of Mecca and Medina is symbolically important, it's not a requirement for one to control them in order to be caliph (neither the Fatimid nor the Spanish Umayyad caliphs ever controlled the holy cities). The conquest of the holy cities by the al-Saud caused alarm mainly because they immediately set about destroying the tombs of the Prophet's family (on the grounds that they had become functionally shrines, and nothing but God is worthy of worship). They were actually planning to destroy Muhammad's tomb itself but there was such a large outcry from abroad that they stopped out of fear that it might trigger an invasion to relieve them of the holy sites.