It's a little different in the US. If you go look at the top-tier schools, you are going to find a lot of kids who are immigrants or the children of immigrants. The elite schools don't really function like they did a few generations ago when they were populated by the kids of WASP legacies. With the exception of affirmative action kids, the best schools are also heavily meritocratic.
Now, the kids of the wealthy do have advantages when it comes to getting into these schools- their parents tend to be educated and they can afford to live in the best school districts or send the kids to private schools. But simply being from a wealthy, prominent family isn't worth what it used to be- look at someone like Paris Hilton, who never went to college and is essentially rich white trash.
If anything, the availability of education to the masses has improved access to the American Dream- 50 years ago, the idea that the children of Vietnamese refugees could go to an Ivy League would have been laughable.
Don't forget ideocratic.