You have already convinced yourself and concluded it can't possibly ever sound good, when it appears that you actually have never heard an excellent tuner properly setup. So our words may not mean much. I suggest you go out and listen; and discover for yourself.
I recently gave a decent mid-fi tuner to a professional musician friend who always used his old worn out 1970s receiver as a tuner through the tape-out, because he assumed like you did. He is now shocked at what he has been missing all these years. He hardly listened to the radio before. Now he has it on all the time, when a CD or LP is not playing.