Yes, resizing one axis resizes the other automatically.
The problem is that there is no ideal screen resolution. Even if you find a way to get rid of the status bar completely, there's the issue of the iphone 5 as well, and other devices if you decide to get it on android or web browsers. I get around all the screen resolution variances by using fullscreen scale and designing the game with extra content off the sides for various screen ratios, but it's not a simple task programming the ui to adjust automatically to accommodate them seamlessly. I'm actually still learning how to do it properly myself. :/