Hand-cut dovetailing was the default until 1860 when uniform machine-cut joints were introduced. But fine cabinetmakers persisted in fitting their joints by hand until the early 1900s, and cabinetmakers in Europe cut dovetails by hand well into the 1930s.
Why are dovetail drawers better?
Dovetail drawers are noted for their resistance to being pulled apart. This is a great advantage for a drawer that is constantly being pulled open such as those in a kitchen, bathroom or closet. Dovetail drawer boxes must be made of wood. Cheaper materials like PVC simply wont work.
Can you make dovetail joints with MDF?
The lack of strength inherent in the mdf is going to mean the dovetails are over-kill and not likely to benefit. As for practice, I suspect the lack of grain in the mdf will end up cheating you out of building any real experience with dovetails.