Determining position of anchor boxes in original image using downsampled feature map

Question

From what I have read, I understand that methods used in faster-RCNN and SSD involve generating a set of anchor boxes. We first downsample the training image using a CNN and for every pixel in the downsampled feature map (which will form the center for our anchor boxes) we project it back onto the training image. We then draw the anchor boxes centered around that pixel using our pre-determined scales and ratios. What I dont understand is why dont we directly assume the centers of our anchor boxes on the training image with a suitable stride and use the CNN to only output the classification and regression values. What are we gaining by using the CNN to determine the centers of our anchor boxes which are ultimately going to be distributed evenly on the training image ?