I think it was an amalgamation of factors, themes and people that led to the collapse of the Caliphate and not one one thing in particlar.
Our greatest weakness is to relinquish the gift of Allah to us; namely to remain on the correct aqeedah and to consolidate our frontiers against all forms of kufr, bid'ah and non Islamic additions to the understanding, interpretation and application of Deen.
On a primary level this means government, unity of thought, cohesiveness of policy and responsible action by those in authority based on the Qur'an and Sunnah.
To the common masses, this refers to knowledge of our religion, the ability and willingness to serve Allah as He should be worshipped, as He should be loved, as He should be feared and (what we have lost today) to believe and hope in His Qadar and still see everything as positive even when our own intelligence look to Non Muslims for guidance and as models for progress.
The Usmani Khilafa had been severely shrinking in size and spirituality since the 1600s. We had begun to lose track of the akhirah, the purpose of a caliphate, the responsibility to Non Muslims, the love of following select aspects of Islam at the expense of a holistic love of all things in religion.
When Muslims start to go towards the Duniya and far from Allah, He allows the Kufaar (His other slaves) to punish and humiliate us (in short they are wake up calls to reform and turn back to Him before it is too late).
By the 1700s it was easier to win wars against the Caliphate and by the 1850s after the Crimean War, it had started to take loans out from western banks and for the first time in 1300 years, riba entered the Muslim world through the Kufaar.
By the 1900s nationalism was the latest fashion trend and the Christian religion an easy tool to attract warring western nations to destroy an ailing empire.
By the 1920s there was nothing left. Ataturk merely dissolved what was already dead. The Usmani Khilafa had severely reduced the powers of all religious leaders in government since the early 1800s and was gradually increasing clauses from French, Swiss, German and even British constutions that was against Islam.
We have only ourselves to blame. But, just as we have fallen, we can just as easily rise again.... if we follow His Deen and follow His Guidance. We can choose to be in the Win Win situation He has promised us or go towards the certain loss Iblis has enticed our predecessors with. The choice is ours and ours alone. The Kufaar can only do so much and ony if we let them. As long as we have Allah and we believe in Him with all our hearts, no one can touch us and we have nothing to fear and everything to gain.