The popularization of the box squat is largely due to Westside Barbell and Louie Simmons, and doing them with a wide stance has definitely been a game-changer for every athlete I've used them with.
There are a couple of reasons they're so great. For one, the wide-stance box squat breaks up the phases of the lift, forcing you to use less weight (which means less spinal compression) while preventing you from using the bounce, or stretch reflex, to get out of the hole.
Secondly, the wide stance puts a great deal of stress on three areas where most lifters are lacking: the hips, hamstrings, and adductors. It's also quite forgiving on the knees since there's less shear force. Overall, the wide-stance box squat is arguably the biggest bang-for-your-buck squat.