Why convolute if Max Pooling is just going to downsample the image anyway?
Max pooling doesn't down-sample the image. It down-samples the features (such as edges) that you have just extracted. Which means you get more approximately where those edges or other features are. Often this is just what the network needs for generalisation - in order to classify it doesn't need to know there is a vertical edge running from 10,5 to 10,20, but that there is an approximately vertical edge about 1/3 from left edge about 2/3 height of the image. 

These rougher categories of features inherently cover more variations in the input image for very little cost, and the reduction in size of the feature map is a nice side effect too, making the network faster.

For this to work well, you still need to extract features to start with, which max pooling does not do, so the convolutional layer is necessary. You should find you can down-sample the original image (to 14x14) instead of using the first max-pooling layer, and you will still get pretty reasonable accuracy. How much pooling to do, and where to add those layers is yet another hyper-parameter problem when building a deep neural network.