Why does head move in Z axis instead of bed?

Every design I've seen moves the head up and down in the z axis instead of the bed moving up and down. Why is this? Don't moving the bed in the Y axis take off a lot of build area? The hotend, extruder and electronics is smaller than the bed so wouldn't it give bigger build area to move it in the Y axis instead? Or am I missing something here ?

It only costs you build volume if the overall dimension of the machine is fixed. While moving the bed in X or Y does mean the overall dimension which that axis can occupy during use has to be slightly over twice the intended build distance on that axis, this doesn't result in an unreasonably sized machine at the build volumes of the most common RepRap designs. As build volume increases, it becomes increasingly problematic.

There's demand for either significant rigidity or mechanical complexity to keep a planar surface level as it traverses in Z. That said, some commercial RP machines and the RepRap Morgan (possibly among others) do move the bed in Z.

Take a look at corexy.

I would say that only prusa styles moves the bed in the Y axis, almost all the others move in in Z.

I have both styles and I prefer the strength and straightness of the Y setting, Having the whole bed holded only on one side gives some flexing to the system especially if the arms are plastic.