Several shocks prove otherwise.
I haven't seen many of those apart from posh houses. Mostly I see the same fitting in every room, a pendant with a shade.
You might splash the hoover, which is all you can do with the razor. Don't forget, you are not in the sink when it falls in. So you have to make a conscious decision to place your hand into the sink full of water with it. That's if you even fill the sink to shave. Most people use an electric shaver to dry shave, and if not, you may just have the tap running, not the basin full.
Well most people dry their hair in the bathroom, either on an extension or the hairdryer cord is long enough to reach to the hall. The mirror is above the sink in the bathroom.