The ceiling is high because they had reason to extract everything in between. 
    The high ceiling with columns like great trees, branching towards the top, is precisely what is described in the book.  It is my theory that the two halls that we see the most of, the twenty-first hall and the second, are higher than average; the twenty-first because it is at the top level of Moria, and the Second because it is the main cerimonial route straight from the gates (the Second Hall is described as being higher and much longer than the Twenty-first, where the branching columns are first described).  We have reason to believe that the AVERAGE level of Moria occupied about twenty-five feet.  That is, in descending seven levels the Fellowship encountered seven staircases of fifty ('or more') steps.  How high would the average Dwarven step riser be?  Six inches is probably pushing it.  So twenty-five feet, less the thickness of the floor needed for structural strength.  Again, the top level (which has natural light) and the main centerline avenue can be much higher; indeed, the Second Hall is so high that it is actually set a level BELOW the gates (in the First Deep) - after crossing the bridge the Fellowship must climb a stair to get to the First Hall.
     And you don't want to get me started on the layout of the North End halls.