Ask a teacher what his or her least favorite aspect of the profession is, and you'll usually hear the same response: grading. Some day perhaps a better idea will come along to evaluate students, but for now we are stuck with As and Bs and Fs.
Please have a look at this article by Corinne Ruff, in the Chronicle of Higher Education. The piece covers a current discussion about abolishing grades, which is actually being tried at some institutions. Here's another article on the same subject, by Steven Mintz, in Inside Higher Ed.
However, most purported replacement regimens seem thin, even when we acknowledge the present system's many flaws.
Interestingly, the model we use today did not arise until the 19th century, at Harvard. The CHE article also includes a discussion of grade inflation (which, by all reports, is much less pronounced at community colleges than at selective universities). It's odd but no one brings up the classic bell-shaped curve, which hypothetically would solve the problem of grade inflation. But the percentage of Fs, if using this technique rigidly, may be too hard to stomach.
One missing aspect of the present discussion is the simple fact that students want and expect grades. To be more precise, students want, and often expect, good grades. They also tend to prefer objective measures, and are more likely to complain about any score that seems impressionistic. That's why essays are so problematic. Not only are they tedious and time consuming to grade, they also represent the format most likely to cause consternation. Those who teach art and music experience the same dilemma of perceived subjectivity.
Presumably in the old days, professors simply gave the grade they believed students deserved, based on …whatever. This may have worked with very small classes, but there is no way such latitude could ever happen again. One is tempted to add that another modern factor is the lack of job security of faculty, especially adjuncts. But professors of yore were never the tenured demigods we may imagine nostalgically.
As for competency-based grading, it works fine with some subjects, but most of the liberal and fine arts, humanities, social sciences, etc., don't lend themselves to such metrics.
The current paradigm is probably here to stay.