To a very limited extent, schools have tried to protect themselves from such cheating by requiring students (or prospective students) to compose writing samples under controlled conditions.
The Law School Admission Test (LSAT), for instance, requires students to write an essay. The essay is not scored; rather, it is forwarded to the schools to which the student has applied. The schools then compare the LSAT essay to the personal statement submitted with the student's application. A gross disparity between the quality of writing seen on the LSAT essay and that on the personal statement presumably raises suspicions that the personal statement was ghostwritten.
Perhaps such measures should be implemented more widely.
While this is an interesting way of comparing, I'd be slightly worried if I were applying to law school. Given that you have a limited amount of time to write your LSAT essay, and an essentially unlimited amount of time to write and polish your personal statement (plus have professors, friends and family look over it), I could see there being a large but legitimate gap between the two.
There are style markers (the writer's voice) that are in the paper no matter how it is edited. This is how critics and editors can tell when a book is written by the real author and when it is ghostwritten. The only way it's possible to avoid this is to digest a lot of material by the original author so you learn to become that voice.
This is also prevalent in song lyrics. You can hear when a rapper, for example, is using their own material rather than a ghostwriters. The flow and definition will be really different.
The Law School Admission Test (LSAT), for instance, requires students to write an essay. The essay is not scored; rather, it is forwarded to the schools to which the student has applied. The schools then compare the LSAT essay to the personal statement submitted with the student's application. A gross disparity between the quality of writing seen on the LSAT essay and that on the personal statement presumably raises suspicions that the personal statement was ghostwritten.
Perhaps such measures should be implemented more widely.