I think that for certain courses, a pass/fail system would be more beneficial, such as classes where marks are opinion based rather than fact based. For example, you can't definitvely give someone a mark based on how good they are in Physical Education or Art, but for things like Math and Sciences, they are based on facts which determine if a student's answer is right or wrong.
With that being said, I don't believe that letter grades (or percentages) could be eliminated from high school education, because students have to take a wide variety of courses.
However, this system could possibly work for certain university and college courses, because marks for the class might be based on opinion rather than fact. The only problem that I see with this is that you wouldn't have any way to know how close you are to passing or failing, and some students would rather just have some sort of system (be it percentages or letter grades) to know how well they're doing.