Why are appliance cords (like a dryer or oven) usually flat?
Parallel cables are designated the NEC as lighter duty than most round cables. Cables that are flat are designated as Type SP, SPT-1,2 or 3, Service duty Parallel or Service duty Parallel Thermoset 1,2, or 3 grade level. Service duty indicates Not Hard Usage, while most round cables (SExx, SOxx, or SJxx) are designated Hard Usage or Extra Hard Usage.
The primary construction deficiency you will find with Parallel cables is single layer of insulation. Hard Usage cables have insulated wires inside an insulating jacket.