Forgive me, but I'm going to rearrange the paragraphs of your posts a bit, to separate two subtopics and make my replies more succinct.
I have always believed that G&T classes/ schools were for "at risk" kids who are intellectually gifted but would not be served by a regular school due to the slower or more average pace of schooling. Would this be a fair assumption?
No, it would not be. The reason for creating such programs is to foster intellectual achievement, not to lower the dropout rate. Only in very specific (and usually urban) situations are gifted children likely to be at high risk for dropping out; in most of the country these programs are havens for the kids who REALLY love school.
When I mean "at risk" I am talking about kids who are not served by their current school and who are at risk of dropping out. This would include G&T kids. That is the whole reason of recognizing them and testing them EARLY.
As I said, an incorrect assumption. The reason for testing them early is to place them in an appropriate learning environment and avoid stifling their intellectual growth. Getting them out of a regular mixed-ability classroom in the lower grades also sometimes has the collateral benefit of giving more instructional time to the rest of the children, in that the gifted child will not be there to monopolize the teacher's attention (which gifted kids tend to do, because most of them are by nature intellectually curious.)
The issue of why the programs exist *is* the gist of the thread, because you are assuming that these resources are designed for at-risk kids, when they usually are not. That erroneous assumption is completely coloring your perceptions of the reasons why people want to get their kids into these programs.
Now then, I agree with what other posters have said about wanting these kids to be challenged and to have better guidance, but I'm going to add one more reason that is specific to major urban districts, and that reason is,
to keep them safe from perceived dangers.
In many urban school districts that have magnet and choice programs, the gifted schools are almost always also the safest schools; the ones in the best neighborhoods, the ones where teachers actually spend most of their time teaching instead of breaking up fights, waking up kids, and writing up mandatory reports about things like suspected child neglect. They are the schools with the most involved and most affluent parents, and generally they are best schools that exist in a given urban district. That whole perspective goes double for the NYC public schools, especially with regard to Hunter. Poorer kids almost never get into Hunter anymore unless their parents are public servants, because the parental involvement bar has been raised too high. As one article put it 20 years ago:
To decide who gets into ''gifted'' programs, which may start as early as the nursery level, schools have traditionally relied on the I.Q. test. The children who do best on these tests, say educators, are those who've had the most ''mediated'' experience - been read to, talked to, listened to, taken on car trips and had every last cow pointed out. In short, the middle-class child.
Three articles on the subject from the NYTimes archive (and note that the first one is 20 years old, it is the source of the quote I used above):
http://www.nytimes.com/1990/05/06/magazine/gifted-children-s-programs-a-matter-of-class.html?src=pm
http://www.nytimes.com/2008/06/19/nyregion/19gifted.html
http://cityroom.blogs.nytimes.com/2010/04/30/10-more-qualify-for-kindergarten-gifted-programs/