Gelatin swell is minimized at a pH of about 4.5, which is where the acid stop bath (acetic acid) would be. Therefore, the tendancy for gelatin to scratch or abrade is minimized.
The tendancy to form stains and to form a dichroic image are minimized by a stop bath. In fact, a stop is beneficial in removing any amine containing developing agent from film or paper. In particular, metol is of note. Metol is slow to remove in water.
Papers develop much more rapidly than films. Therefore a stop is much more effective in getting a uniform image in paper than film in some cases. This is to be noted in the posts above. It takes 10 minutes or so to develop films, and some take longer depending on developer. Paper is moving at 10X that rate and must be stopped in a shorter and more effective fashion for just that reason.