Whenever I see overt double redundancy, I'm immediately tempted to test the system.
In this case, a ground fault plug, plugged into a ... GFCI outlet. I'm at a hotel this week, and I was seriously tempted to throw the hairdryer into the sink and see which one tripped first.
In all fairness, there are good reasons why they did this. Per most building codes, a GFCI outlet must be installed if the outlet is within 6 feet of a sink (or something like that). And, of course, the hotel chain wants to be safe, so they only buy hairdryers that also have a GFCI plug.
But seeing the two together hints at the overbearing safety culture that continues to run rampant.