I like clearly seeing what the next one or two pitching moves a team has. Do you bat this guy with so and so warming up? Is so and so warm? He only threw 3 pitches. You then know why the catcher is out on the mound killing time.
When you hide the bullpen, new pitchers magically appear on the field ready to go. Sure, you can read on a message board that this guy is warming up - but you don't know so many other details about it.
Bullpens in the of like Fenway provides the added bonus of having a short wall in the of. You really can't have that with fans behind the wall. Rather there is a 8-10' minimum wall. Everyone loves guys catching fly balls and falling over the wall. Remember the famous picture with the security guard's hand in the air?