"Aren't these questions a good way to see how we'll people think on their feet or react to an awkward or stressful situation? "
They would be, if they were related to the task at hand. If you want to throw someone off your game (That is, see how they react in the context of the job they are applying for), use industry specific jargon in an incorrect way, or ask them to use a pen and paper to draw something related, be it a map, an object or a relation between a division of some sort related to the position (i.e a word problem solved in graphic form).