I don't think the buzz stop is ugly, it just kills part of the characteristics of the Jaguar/Jazzmaster sound to add sustain. That part is the slight harmonic drone of the extra length of string behind the bridge (sympathetic vibrations), to my ear it adds a tad bit extra harmonic content to the sound that's not present on other guitars, and the Buzz Stop removes that because it kills a direct path to the part of the string that actually makes the sound. It's like a force-feedback effect, you pluck the string in front of the bridge, and particularly on the lower strings, the energy making the string move in front moves the one in back from momentum, and that one produces an inaudible (most of the time) tone that you only know it's there when it's not.
