Here's Sam Hinton with a perfect example of why one would get a natural minor harp rather than playing in fourth position:

http://www.youtube.com/watch?v=P93ctZNRSl8

The chording is only possible with a natural minor tuning.

He also demonstrates swapping between harps mid-tune, either to change key or to get additional chords. In the first two selections, he uses two harps, in the last, four!