The only two positive aspects that come to mind in printing a thinner negative are printing times and the grain considerations of smaller film formats which has already been mentioned by Eric and myself. These are both valid considerations.
The possible negative aspects are concerned with the characteristic curve of the paper which is exactly opposite of film. If the contrast grade of the negative were too narrow. One would seemingly lump a greater portion of the shoulder and toe film values onto the corresponding opposites of the paper. So, taking this to a ridiculous example for illustration purposes, if one had a three zone contrast range and attempted to spread it onto a six zone paper range the film values would be spread to some degree, but the values would not be the same as if one had developed the film to the six zone contrast range. The tonal range would not be as smoothly represented on the print.
Ideally, in a perfect world...we would take the time to determine the characteristic curve of the film that we were using and in exposure and development decisions we would have the greatest portion of the scene luminescence placed on the straight line portion of the film. We would also determine the characteristic curve of our paper to the extent that we placed the camera negative values on the straighline portion of the papers characteristic curve. When we are successful at accomplishing this, the print will have reached a much greater portion of it's true potential in tonal representation.