One of the main criticisms of gaming on the iPad (or any iOS device) is that there is no tactile buttons for games that feature a directional pad, or virtual joystick; one example is Super Mega Worm.
That includes twin joysticks, bumper buttons ... Connecting an Xbox controller to your iPhone or iPad might give you a warning message that claims the controller can "affect" your WiFi or ...
It was a good starting point: inexpensively purchased off eBay with suitable arcade-style joystick and ... the screen is a replacement iPad 2 LCD combined with a controller that accepts HDMI.