I was once a critic and a journalist. I left the field because, from experience, I learned that there is no such thing as pure objectivity.
If, for example, you confined judging piano competitions to faithfulness to the score, you'd still run into issues such as "How fast, really, IS presto?" Isn't presto relative to the preceding allegro? And even if composers, such as Beethoven, insert metronome markings, isn't there also the variable of the particular piano and the lightness of its action that Beethoven would have written for? Didn't Schnabel show us that it can be a real scramble to realize Beethoven's markings on a modern grand?
In truth, we bring unconscious judgment to everything we hear. It informs our choices beyond our awareness, no matter how much we insist we are being "objective." We see through eyes and hear through ears that send the messages to our brains where vast amounts of stored experience and education process and distort. Eyewitness reports in courtrooms are notoriously unreliable. Why? Because our uniqueness as individuals colors objectivity. It distorts our perceptions.
Even in science, where the most scrupulous methods of observation are mapped out, there is no real objectivity. It has been found in quantum mechanics and beyond that the very fact of the observer alters the observed.
Personally, I don't think we need critics. I don't think we need competitions, either. They are both only barely-disguised marketing ploys. Tacky. As Bartok said, "competitions are for horses, not pianists."