Sleeping is a lot easier on a comfy padded bench than it is on the floor, so it happens a lot less than it otherwise would. Preventing sleeping isn't just to the advantage of the people who want to sit down without having a sleeping man taking up four seats, it's also to the advantage of the people who would otherwise be tempted to take a nap that they know they shouldn't (because they need to catch their next flight).
Oh, and some people do want to sleep in airports -- cheapskates who don't want to pay for hotel rooms. Check out "The Budget Traveller's Guide To Sleeping In Airports":
I'd also imagine more people would avoid sleeping on the floor for cultural reasons too. We perceive someone sleeping on an airport waiting bench to be a weary traveler. Seeing someone sleep on the floor in a very busy place communicates vagrancy.
Oh, and some people do want to sleep in airports -- cheapskates who don't want to pay for hotel rooms. Check out "The Budget Traveller's Guide To Sleeping In Airports":
http://www.sleepinginairports.net/
for far more information than you ever wanted about the best places to sleep at airports all around the world.