However, after seeing so many folks doing this I began to wonder if I am missing something. So, is there a legitimate training purpose for shooting so close? Wouldn’t it be better to shoot at greater distance for self defense purposes? Just curious what distance you guys recommend for general self defense practice?
As pointed out, you need both speed and accuracy for effective self-defense.
Past a point, shrinking your groups isn't particularly productive if self-defense is your only goal. If your groups get too small then you should take that as a cue that you need to increase your speed a bit.
Find a good "practical" target (examples below) and train to keep all your shots in the center zone of the target (9 or better on the target with marked scoring rings). As you get better you can increase your speed and also gradually move the target farther away.
Ideally you want to learn what you need to do to achieve consistent center hits while shooting at speed and at various ranges. Up close you can use the entire gun as a "sight" and get acceptable hits while shooting very rapidly. As the range moves farther out you may need to slow down a bit and pay more attention to the sights to keep making good hits.
Clearly you don't want to slow down TOO much as range increases because speed is still important, but you don't want to try to go too fast either or you'll stop making hits.
Obviously, if you're involved in some sort of organized competition, you may want to train for specific skills involved in that competition. But for self-defense, small groups at long distances probably aren't the ideal training standard because speed needs to be part of the equation.