What's the Bible verse? "Something like Why do you look at the spot of dust in your brother's eye? But you do not see a big stick in your own eye?"
The reason that the Saudis will probably not change anytime soon is that the average Saudi is relatively happy. The surveys that have been done over the past 20 years or so say that Saudis
rank above most of Europe and Asia on all measures of happiness.
One of the reasons that Saudia Arabia survives in this manner is that they are largely a socialized welfare state where most of the citizens have a comfortable life based upon government welfare and stipends. The stipends vary- anywhere from $700 for the lower tier of people up to $200,000 a month for Al-Saud family members. The inequality is one of the most common complaints but most citizens overall feel that there is a good social safety net. From their viewpoint, they have stable families, their children well cared for, their healthcare is free, their education is free, they pay no taxes, cost of living is low (there are lots of subsidies on many items) and they feel safe.
Westerners look at the Sauds and say, "Oh, what a terrible country" but the Sauds are happy. Because of the socialized welfare system, they don't have a reason to change. If the billions of dollars that pour into the Saudi economy from oil exports were to dry up, there would be a major upheaval in the society there but until then, change will come very slowly.
Some of the things that human rights organizations criticize the Sauds for are valid. It's a terrible place to be a foreign worker and non-citizens who encounter the Saudi criminal justice system are treated very poorly. But honestly, the Saudi kafala isn't much worse than the US immigration system. Most of the complaints of the Saudi foreign worker system have to do with how companies treat the workers, not how the government treats foreign workers.
In an earlier post, I made a distinction between Sharia's rules around marriage/family versus Sharia's rules around justice. The Saudi system is a good example of why Sharia is a terrible way to conduct justice. Saudi Arabia has a very weak criminal justice code, so judges are free to mete out punishment as they please. Some use Sharia and others just make up punishment based upon a whim. This is why there's so many stories about beatings and unfair imprisonment. Tradition has been that the Qur'an and Sharia are a criminal code, so they never really formalized a penal code based upon law in the way we understand it in the West.
Don't expect the US to pressure the Saudis to change- the US still considers the Sauds a key ally in the middle east; they know that if they are too aggressive, the Sauds will take their money and oil elsewhere; and it's a little hypocritical for the US to criticize the Saudis over things like the social inequality and the death penalty when the US has the same stick in their on many of these issues.