That was also always my feeling, but now I’m not so sure.
What seems to be happening is that there are too many very high achieving students for the T-20, and many students have only these as their choices. These colleges accept fewer than 30,000, which is about 1% of all high school graduates, and about 3% of all students applying for 4-year colleges. About 12,000 of these places are going to students with the “big hooks” (athletes, legacies, kids of faculty, and donors). Moreover, because there are many well to demonstrate “excellence”, there are enough students who are “top 1%” in any category that there are likely not enough places in “T-10” or “T-20”, or even “T-30” colleges for all of them. This is especially true if you take out the top publics, which are much larger than most of the private “elite” colleges (because OOS tuition will often remove these from consideration).
In almost every case where I seen here that a high achieving student has been rejected from “every college”, all the colleges were colleges with acceptance rates of less than 20%.
Because of the run on “elite” colleges, there need to be some 200,000 places for students who are the the “best” 10% (by any measure that one may choose). So there are simply not enough places for all. Of course, it is more complex - some colleges are moderately selective overall, but very selective in some fields (like UIUC and CS), other reserve places for their state, so, Michigan have very different acceptance rates of in state versus OOS (as do UVA, W&M, UNC, and some others), so very competitive students from Michigan, for example, is not likely to be shut out of U Michigan.
So while it is not all that common, It seems to me that highly competitive students who have been rejected from all of the “elite” colleges to which they applied are increasing in number, while applicants who have been accepted to multiple “elite” colleges are decreasing.