"Can you please explain why hard-drives follow a flying head approach? Why don't they just perpendicularly fix the reader above the disk, rotate the disk and then use a linear actuator to move the reader back and forth - exactly like optical drives?"

The head is only "flying" relative to the platter. A hard drive works pretty much like you describe -- a short stack of fast-spinning platters and a read/write head on a swing arm that pivots back and forth over the platters.

A pic: http://msuweb.montclair.edu/~maciakl/blog/img/hd.jpg

They are child's play to take apart (http://turmon.org/Images/celeste-disk.jpg)