Random thought, With current communication technology would superhero team headquarters even be necessary?
Plus with characters like Superman, The Flash, and Green Lantern, etc, being able to meet up with someone any place in the world quickly, what is the point?
Its just makes them a public target for super-villains. Now the lower power level teams like the Titans I could see but not the JLA. So in that way The Hall of Justice works as their only "headquarters". Its a public embassy more than anything.