Non-traders have a smaller reach and can only accept a sell order or accept a buy order, not match them up. Though you can easily simulate the matching by accepting the buy offers first, then accepting the sell offers. I guess that's not a real advantage of the Trader.
It is, because the trader doesn't have to be a region lord, i.e. he doesn't have to ever actually store the food anywhere, not even for a short period of time. He also doesn't have to have the bonds on hand to do the buy deals, even with empty pockets he can broker a deal and make a profit.
The first part will become even more important once we add transport delays.