Will it make a better result if the image was cropped equally from all edges ?
Not unless you consider decapitation an improvement.
Is it too difficult to resize the image first just using one dimension (e.g. height) and then crop the remaining off the sides if necessary?
That will only result in something that will fill the screen in the rare case where the aspect of the original image is wider than that of the screen.
The problem only occurs with tight head shot portraits (i.e., only a head, so nothing can be cropped without losing part of it). A solution would be to show two side-by-side and crop from the right, but that would only be better for this kind of shot. A portrait that includes a whole body or even a classical head shot will look fine—and usually better than the side-by-side solution—when cropped from the bottom.
I'm sure the problem will eventually be solved using face-recognition.