Why are post offices always a target for robbers in anime?
Japan's post offices are banks. And the Japanese postal banking system is nothing to sneeze at. In fact, in 2008, Japan Post Bank held more deposits than any other bank in the whole world! 

It is hence unsurprising that shows set in Japan, like Index and Sword Art Online, might feature robberies on post offices. There's a lot of money to be had there!