Why is it more common for consumer level FDM printers to move the extruder on the Z-axis (For example, the Ender 3) while the bed remains at a fixed height, than to have a bed that moves up and down on the Z-axis?
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The reason is economics, building cheap printers for the masses requires the use of as less material as possible; this keeps the price down.
A bed that moves up and down requires a sturdy construction and usually more and more expensive materials.
If you look at the Prusa i3 style printer, the bed moves in Y direction while the X-Z is a single plane perpendicular to the Y-axis. This allowed printer designs to have a single upright frame made from acrylic (not the best solution, but cheap) or steel plate (expensive due to the cutout and waste material) or aluminum profiles (value for money solution). If you need the bed to go up and down, you need to constrain the X-Y plane high above the build plate (e.g. Ultimaker printers, Hypercube, etc.); this requires a stiff frame and hence more material.
Do note that e.g. the Voron 2.4 although a boxed up printer, has a fixed bed and a moving X-Y plane. This requires even more materials and is even more expensive.
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