Why does a bike frame have to be above 56 cm usually to fit 700c tires?
The real issue is in the top tube length.  Basically, for shorter riders you need to move the handlebars closer to the seat.  But then you have to deal with the wheel possibly colliding with the pedals ("toe strike"), changing the head angle or the fork's rake, which compromises the handling, and/or having a proportionally longer top tube than would otherwise be indicated by the seat tube length.

Rodriguez Cycles did an excellent multipart essay on choosing between 650c and 700c wheels for road bikes, and the illustrated Cliff notes they provide should prove illuminating.