Ask an employer that question when they inquire about your GPA and see what their response is. They have a stack of resumes on their desk and want to know what sets you apart. The only way to measure that you know how to do what you say you know how to do is to provide documentation regarding your experience or, if you are just entering the workforce, provide the employer with a record of your academic performance. The typical catch-22 that you will most likely be faced with is that you cannot gain any experience unless you can get hired in the first place.
There is no motivation for students to attempt to achieve a well rounded education without measuring all aspects of their entire academic performance. The student may simply choose to focus on the subjects that they find interesting or none at all if it suits them. If as a country we are making a push to achieve higher math scores (for example), you can forget about that ever happening without a grading system in place because most students do not like math. The one argument for abolishing grades that fails miserably is the statement that without testing and grades the student can concentrate on the material and not have to worry about taking grades and taking tests. Well, if the students are concentrating on the material then they should have no problem passing a test. The retort to this would then be that some students are not good test takers. That is why homework should also be subject to grading.
Grading benefits the student as it points out their strengths and weaknesses. A student may not be aware of the fact that that they do not understand a concept that they thought did. Grading allows them the opportunity to go back and correct the mistakes that they made and gain a better understanding of the material. The current administration in charge of the Department of Education is more concerned with placing the certificates of achievement in the hands of students than actually making sure that they understand the material. It is more important to them that everyone have a high school diploma and a college degree regardless of what they actually know. This is reflected every time a state lowers the requirements for standardized test scores so that they can continue to receive funding from the federal government. So fear not! While grades are here to stay, the tests are getting easier.