People that can pass of as white are more often of mixed heritage. Even then its really rare for them to be passable into the majority racial population. It all depends on their racial/ethnic composition. If one is half-latino/half-North African/levant and half-white, chances are they're going to be passable and most likely identify as white. Even the U.S census considers people from MENA as white. There are also white-Hispanics. But same can't be said of people that are a mix of African-American + Caucasian. See Barack Obama, Jordan Peele or Keegan-Michael Keys as examples. What you consider "high" for passable are still a small fraction of the minority population.

Also passable isn't a think most people do these days. At least not since the 1960s where racial barriers were much higher. These days people of mixed heritage will most likely identify with the minority side of their heritage. (For many reasons).

As a Brazilian friend of mine once told me - Racial classification and categorization in the United States is just weird.