Engine does not have to be running at touchdown! Speaking for myself I was trained by a pattern pilot...his reasoning was that it was one less thing to worry about for a student pilot trying to get the landing setup just right...and well taught habits tend to stick.
However, flying a Webra 1.45 I personally find much more control when I have the engine running at touchdown as the large prop acts as a brake. The few times I have had to land dead-stick I found that the plane floated on much further. And the Webra 145 is a lovely engine to land...back three or four clicks from the centre and the plane will come smoothly in on a very reliable engine tickover. Interesting that it appears to be the four-stroke guys who tend to kill the engine isn't it?