Why is stroke order important when writing Chinese characters?
The stroke order is important, yes. The main reason that explains why the stroke order is so important is that the it helps to write the character correctly, with better speed and in an easier way. 

Pick a character, and try to write it with the official stroke order, and then with another one: you'll find out that in the second case it will be sometimes harder to write it and mostly it will come out with a different shape, i.e. incorrect shape, and also ugly sometimes. This is because when using the official stroke order, the character will appear with more harmonious proportions and therefore, more beautiful.

Also, I'm not sure the following are "official reasons", but I suppose that:


it helps to memorize the character and retain it too, because your muscles "remember" the movements and so does your brain;
when reading someone else's handwriting, the shape changes a lot and the movement of the pen/brush can help you to read since you know the stroke order.