while the ROM may be shortened with a wider stance, that is not in fact the sole reason for using a wide stance squat.
The muscles of the posterior chain are generally larger and have greater potential for strength. A wider stance squat allows you to more fully utilize the large muscles of the hamstrings, glutes and lower back in the lift.
Now, most people have serious weaknesses in their posterior chain and are quad dominant, requiring a lot of retraining in order to take advantage of the more powerful prime movers used in a wide stance squat.
Squat suits happen to also work best when using a wider stance as they support the hips better, and a wider stance stretches the seams further.
Talk of targetting a muscle is less about powerlifting and more about bodybuilding, as the target of squatting in powerlifting is to squat more weight.
Now all that being said, there are limitations to wide stance squats. Hip mobility/flexibility is huge, as is ankle flexibility (greater dorsiflexion allows greater depth). If you are unable to open and keep open the hip during the squat you'll shoot forward and dump or GM the weight, reducing your ability to squat big numbers. If you are quad dominant/hamstring weak you won't be able to sit back into the squat and support the weight/maintain balance in a wider stance.