Bass, my interpretation about why you would espalier fig trees like that would be the same reason for grapes: The closer the fruit is to the main trunk and root system == the shorter distance nutrients must travel to get to the fruit == more goodies directly to the fruit and less energy used to get it there. Less energy spent means more energy to put towards fruit production.
This is my non-professional opinion about why you would also do this for figs. I've heard many a vineyard keeper say that deeper roots and well-espalier'd vines = more concentrated fruit flavor on a healthier piece of fruit.
Just my 2¢, if anyone knows this is myth or urban legend or something, let me know.