I used an electric razor when I first started shaving, and switched to a wet shave maybe three years ago, purely for reasons of convenience. I hated fumbling around with a hazardous-seeming power cord or keeping a cordless razor charged - invariably, I would forget to plug it in, and it would run out of juice halfway through a shave.

A safety razor obviously doesn't have that issue. To me, the closeness of the shave and the cost savings are merely side benefits; convenience is the main factor.