Why do I need to turn my crankshaft after installing a timing belt?

Yes, it's absolutely necessary. As you state, the primary purpose is to check the timing. It is far better to do this by hand and ensure the timing is right rather than to start the engine without it being in time and it trashes your entire valvetrain. When turning the crankshaft by hand, you can feel if there is any binding, which will allow you to double check things if needed. Also, just because you think you've gotten everything right doesn't mean it is. You can easily have one tooth off and it appear good at first. By the time you have turned it two full crank revolutions, everything will be as it is going to be with alignment. If something is off, it will show itself when you've completed this step. Belt tension in the wrong place us usually the culprit and can throw things off. Turning the crank two turns is a VERY valuable step in ensuring everything is right, so don't skip it.

Also, in reading the step after the step you've stated, part of the reason for turning the crankshaft over two turns is to ensure the tensioner is pre-tensioned correctly, then you torque it in place. This ensures your belt will stay in place as well as not get worn out too soon.