I've had a 14-inch barrelled Remington 870 AOW, and found it to be a bit slow for the second and followup shots. Agreed, a 12-to-14- inch barrel can indeed be handy on a shotgun, but good control pretty well requires having the full buttstock on behind, not just a pistol grip.
Also, muzzle flash from a shorty can lead to flashblindness of the user at night. Since I had mine as bear insurance, that wasn't much of a consideration for me, particularly as my first round up the spout was a dragon's breath load, which I figured would serve either to discourage any bruins I ran into at night, or to signal to aircraft passing overhead.
I've been saving them because I know that when I get older I'll be too lazy to walk up to what I want to set on fire.