Why does heapify swap the top of the heap with the element at the bottom of the heap?
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In a max heap (assuming it's represented by an array), the top of the heap (ie. the largest value in the heap) swaps with the last element in the array (ie. one of the smallest values in the heap), the last element is removed, and then the new top-of-the-heap element swaps with other values to settle back into its proper place. 

Instead, why isn't the top element just removed and then other elements can "fill in" for the the heap?