Good summary Grinity.
One thing I would add, in the US as in the UK, is that many independent schools have from 15-30% of their students getting partial or full tuition support from the school's endowment funded by the wealthier families, alumni, and local supporters.
This support enables families of limited means to enroll their children in schools previously reserved for the very well off.
This also raises the caliber of the student body overall and greatly enriches the learning for all the kids. A number of independent schools have seen their overall test scores rise as a result of the opening of the selection process to a larger applicant pool.
Most colleges in the US do have a test-out policy that allows for students to bypass prerequisite classes via testing. This is a different policy from granting credit for AP tests. Students will sit for the class final or a standardized test and must score over 90-95%.
There is also a test given in the next to last year of secondary education, or the 11th grade, called the Preliminary SAT. The top 4/10% of those test takers usually become National Merit winners and most state schools and many private colleges offer full or partial scholarships for these students.
