Unlike in Christianity (specifically Catholicism), Islam is much more decentralized. This means that if you control religious sites or places, you will have much more legitimacy. This is why Islam split early after its creation and why there is a fanatical power struggle between the two most powerful countries in the region, Saudi Arabia and Iran.
To give context, the Ottoman Empire was falling apart (no surprise there). The British took Egypt, Libya was lost to Italy, Most European territories in the Balkans were lost to various countries. The Ottoman Empire was a skeleton, surrounded by voracious vultures waiting to carve their stake in the Middle East. That time came in the Great War, and the Ottomans were crushed.
This power vacuum would lead to a power struggle between the Kingdom of Hejaz, a more moderate faction which had the promised support of Britain and France, and the Sultanate of Nejd, a more radical group who had attempted to unite the Arabian peninsula twice by now.
Hejaz and Nejd would be pitted against one another in a fight to the death, with Hejaz ultimately losing and being crushed by Nejd who would end up forming the Kingdom of Saudi Arabia.
Why is this important? Remember the previous mention of Islamic decentralization? Well, with Saudi Arabia controlling the Hejaz region (which contains both Mecca and Medina), it gave them a lot more legitimacy. By proxy, their ideology and religious custom would also take center stage, Enter Wahhabism, a more ultraconservative, fundamentalist, and austere adaptation of Islam, and it was just justified in the conquering of a religiously significant region. The Islamic World would grow ever more radical with the Saudis using their money to spread their influence like tentacles going so far as to fund America's monstrous debt. Now, this new radical approach would validate more radical approaches and beliefs of Islam. Osama Bin Laden was a Saudi rich kid. The Saudis were purported to have funded 9/11. The Muhajadeen were supported by the Saudis. Their oil money spoke for them, and people wanted a piece.
In my opinion, the succeeding of the Kingdom of Hejaz would have been better for both Muslims and the West. With a more moderate kingdom, they would be more willing to work with the West, the Islamic World, and the East. They would be more open to reform, freedom of speech, among other Western virtues. They also won't meddle with the oil market (or are less likely to) as Saudi Arabia used their vast wealth accumulated from oil as a catalyst to destroy their competition with countries like Venezuela and Russia being especially affected.
Overall, a more moderate Hejaz kingdom would be better off for the stability of the Middle East.
Would Iran not be fundamentalist?
Most likely not. Iran fell into an authoritarian theocracy for different reasons than the Saudis winning this war against the Hejaz. The main things that led to Iran's revolution (the unpopularity of the shah, British and American interference in their oil fields, among others) wouldn't have changed as the things that caused their inception would still exist.
That's my personal opinion. What's your thoughts?