In the institutions that have qualifying exams, 0% who fail them go on to earn a degree. I joke, but it is true!
I can't speak for all disciplines, but for those that take an apprenticeship (as in the sciences), quals are less about the exam and more about the process. It is often (but not always) the case that quals are taken very well into the graduate process, and by the time you get there, your committee already has high confidence that you will pass. Rather, the quals are meant to force you into a period of intense scholarship, reading, and reflecting that will shape the rest of your career.
I don't know of any research on the relationship between qual exams and academic success, but I suspect that the process of having quals does at least two things: 1) provides for an objective system to weed out students who should not progress forward and 2) provides a platform for successful students to focus for an extended period.
Remember, the prestige (of the university) standing behind your degree is connected to the quality of people who hold it. Having high standards and a difficult process (quals) only strengthens the reputation of the institution and by association, your degree.
So perhaps the better question is whether or not places that do not require qualifying exams award degrees to less prepared students?