I believe that what GeoGraphics is doing here is maintaining the GeoProjection while allowing you to increase the ImageSize of the Graphics bounding area that it is being placed in. If it were to stretch the map in the vertical direction then it would alter the GeoProjection that it is using: so it overrides that. To fill more of the area you would need to increase the amount of physical earth surface that GeoGraphics is plotting. To do this you use GeoRange as in
Though you are completely correct, it is very cumbersome; because you want to size your plot in general. I don’t want the find the exact georange such as to get a 500*800 image.
Giving an image-size, and geocenter, and a georange (in meters for example) should be enough to give me an image that fits (at least) this range).