Yes, the house of Saud has been resisting modernization for too long, and now that they finally start moving in the right direction it may be too late. Saudi Arabia has been in dire straights for years ever since the oil price collapse. The recent push to modernize and cease being almost solely dependent on oil exports is ineffective since there is not enough educational and practical infrastructure in place.
With the democratizing effect of the internet, it is only a matter of time until all archaic forms of government fall by the wayside. Thanks to this technology, the moderating effects of Western culture are able to bypass otherwise impenetrable borders and infect the minds of oppressed people in other parts of the world. They will see the freedom other people experience and they will want it for themselves.
Given the wealth of the people of Saudi Arabia, I'm surprised they haven't given up their medieval ways and the royalty already. I think as time goes on, more Saudi Arabians will want to be a part of the modern world instead of being stuck in the past and they'll modernize their country,
1960 was a long time ago. It was half a century ago. Although there may still be some who support the Shah of Iran's position, the sentiments of many of the people of both of these countries has changed. 50 years is a long time and many who were even born at the time have grown and entereted the political arena with ideas and opinions of their own.