>Why didn't they just fly it there?

They did. In 1903 they achieved the first controlled powered flight in Kill Devil Hills. If If my memory serves correct, it was late in the season, and having achieved their objective after three long years of camping in that miserable location they packed up their plane and went home. It was the last time they worked at that location.

For the next several years, until their contract with the US army they flew at Huffman Prarie in Dayton Ohio. There were lots of witnesses but strangely the world wouldn't really know of their success until 1908.