I don’t buy it, yes without those events, the Muslim worlds would be different, but different doesn’t mean better. The Saudi are not going to end up as super liberal Democrats no matter what happen. A coup in Saudi Arabia as we almost saw could replace the House of Saud with a military junta, and it’s hard to not see that as a improvement. But if we look at Libya another oil rich state, the replacement of the monarchy only resulted in a deranged madman taking over. Saddam Hussain while better than Ghaddafi was also still a major destabilizing factor in the region. It’s also next to impossible to imagine that Iran won’t have coup and counter coups, the Revolution was what’s the 3rd or 4th violent change in power in Iran in the 20th century. As for India I have also a hard time seeing the partition being avoided, and I suspect if it was avoided, it would not result in unified India being a happy happy fun land. Instead we could see a more unstable India with even a higher degree of regional civil wars and ethnic strife than in OTL.
Also even without Saudi Arabia we still have the Muslim Brotherhood.