They arch because you can't design a flatbed trailer to be ultralight and rigid. They need to arch when empty so they flatten out when loaded heavily. Vans and reefers are semi-monocoque which means they have walls nose doors and a roof to contribute to structural rigidity so they can be straight loaded or empty.
it is for structural streingth, and weight resistance... it is harder to break a arched structure than a flat one. so it can hold more weight than a flat one. when weight pushes the trailer flat its built in arch pushes up providing resistance. where as a flat trailer would bend downword instead of being flat when loaded.. making it easier to break under the stress of travel if not imediatly when loaded. damns are arched for the same resion. what is the strongest structure? a flat surface or a arched one? a arched one.. something the romans figured out a long long time ago.