No. Grades are needed. They should not be abolished. I respectfully suggest you haven’t seriously thought about pedagogical utility of grading in helping students improve their math skills.
The beauty of math is that it is has answers that are right or wrong. You can argue with the English teacher who clearly did not appreciate your brilliant reorganization of the sonnet form. But you have to concede to yourself you made a misstep in your math derivation when you see your answer is wrong.
There is a pedagogic value of grading that can be leveraged to improve math skills. As a teacher of first year university students, I go over each quiz as soon as I can, while it is fresh in their minds. I emphasize common errors. There are lots of groans. However, students seem to have a strong memory of what they did wrong. The capable ones don’t make the same mistake again.
Grading also solidifies the sense of achievement when a student does well. I try to make exams hard enough to make them feel good if they get a high mark. It also forces those who were trying to coast to realize they may have to work a bit to get a decent grade. Some of these students have told me later they had never really been challenged and have never needed to work hard. These are students who may be pushed to achieve their potential when motivated by desire to get a good grade.
So I agree teachers should not make grading the ultimate goal of the class. Learning is. However, grading can be a useful tool to promote learning.
That is my experience.