No, I'd say the objective of all cultures should be the well-being of their members. Or, perhaps to state it differently, the members of cultures should value that culture proportionally to how it improves their well-being.
If I were to be standing behind Rawls' veil of ignorance, I think I'd much rather be born into some cultures than others, and I don't think that view can reasonably be put down to bias based on the fact that I'm not actually behind the veil of ignorance and thus am biased toward the culture I was born into. Certainly some of it can, but not all of it.
Things like political/economic/religious freedoms really do matter to human well being, I think. And they have not just direct impact on people's lives, but indirect impact on how societies can improve overtime, correcting their mistakes and helping people to cooperate to build the sorts of lives that they want to live. The same is true of different shared sets of values.
That's a reasonable viewpoint, and is probably the predominant one among contributors to this thread, so it's nice to have it spelled out. But it's a bit idealistic. In actual cultures, the goal of the culture is a component of the culture itself. We see people enthusiastically supporting and participating in these cultures even when they're suffering from its practices. Warrior cultures are a simple and common example. (We haven't even left behind all aspects of warrior culture in the U.S. For instance, universities and public schools are supposed to be about a culture of academia but the sports teams keep taking the spotlight and a surprising share of the funding. Bullying is hard to stop because the same administrators who write anti-bullying policies often look at actual individual bullies and perceive, from deep in their evolutionary heritage, admirable alpha leaders who will someday bring much honor and plunder back to the village.)
The purpose of Amish culture is to preserve a particular way of life. Judging its success in terms of how well it accomplishes that, I'd conclude it's not failed, but it's not fully successful either, due in large part to outside factors (an increasingly connected and technological world) that make it more difficult than it used to be.
The purpose of Chinese culture is to maintain internal order, which is at least partly understandable in light of the consequences of those periods of Chinese history when the government has failed to do so. We can view the past seven decades there as a period of success, or as a brief respite amid a longer period of chaos, depending on time frame (as Chinese history is long). Either way, continued future success is uncertain, but again that's partly due to the times we live in.
For the actual topic at hand, as far as I can tell, the purpose of Arabic culture is to exalt the Prophet. It's been fantastically successful at that; the Prophet is constantly and widely exalted in numerous ways, from elaborate daily practices to acts of extreme devotion and martyrdom (some of which are also terrorism) to the raising of unprecedented monumental structures. The goal of exalting the Prophet isn't better accomplished by giving everyone a comfortable standard of living, but rather by concentrating wealth in the hands of a few emirs and kings who can then fund lavish temples, impressive monuments, and global fatwas against dissing said Prophet, while also enforcing the laws he supposedly issued.
We say to that, what a waste, but go back 1000 years and substitute the Savior for the Prophet and that's what European culture was all about too.
But what about individual well-being? Most of the subjects of the Son of Heaven, the Elders, the Imams, or the Village Chieftain will all tell you their cultures are best for everyone's individual well-being, through (more or less respectively) an orderly society, adherence to specific traditions, rewards in the afterlife, or the spoils of victorious raiding.