What difference will it make if universities start accepting students at random (for 10 years,or longer)?

If were only talking about selective graduate programs, my response would be: Mediocrity will rule. These graduate majors would no longer be able to offer challenging programming, because in each incoming class, there would be a group of students that would not be academically prepared for that challenge. This is why selective admission exists. A bar is set because people at or above that bar are the ones most likely not only to succeed -- but thrive -- in a particular program. Without that bar, these selective programs will no longer be able to do what they do best. They reverse may also be true: If a selective program adopted this policy and decided not to accommodate the academic abilities of all incoming students, the dropout rate and/or academic probation rate would increase. Mediocrity wouldn't rule, because people would be forced to leave the program that couldn't hack it, but the program would be intentionally putting a portion of it's incoming class at a high risk for failure. And that's bad business, all-around.

Assuming the course content/speed isn't changed and candidates apply to schools well above their ability level, you will have highly elevated drop-out rates and a correspondingly low graduation rate for undergraduates and master's.  The course content and delivery speed at elite universities is tuned to the caliber of their incoming students.  By making the student quality random, you have now introduced a large population that simply won't be able to keep up. I once wondered what makes a top-3 electrical engineering program highly ranked besides the quality of the students, and since this was in the early days of the Internet, I went looking.  I looked at the engineering curricula: the number of courses, required courses, and the difficulty of topics.  I also looked at the course content.  There was a significant drop in the number and difficulty of courses when compared to schools ranked at 20-25 and lower; some courses were not required or offered.  The notable one for me was semiconductor physics, which was required in my program but very few others.  (It had a very high failure rate.)  The course content was also less at the lower ranked schools, sometimes little more than half of the top schools. As for research, you can't make a good researcher out of someone that doesn't understand the fundamentals and the basic assumptions.  I've seen several failed attempts.