Is it possible to need an expander on top and bottom jaws?

The ideal arch shape is a Roman Arch (like a horseshoe shape) and many people have what is known as McDonald's arches - exactly what you described (narrow in front and wide in the back). Expanders can be used on both upper and lower arches to round them out more and this creates more room to align teeth. More adjustments are done to the front half of the appliance since it's the front half of the mouth that needs more widening.