"The menus have to be navigated with a keyboard & mouse, but game is playable with controller".
That's not true. You can take the keyboard and mouse defaults, plug them into JoyToKey, and play the whole game with a controller.
Profiler programs have been around for decades. Some of them haven't been reliable. Some of them have frivolous proprietary restrictions (ie, Logitech) but profilers do exist.
The only way to render a PC game controller-unfriendly is to make a game use an entire keyboard, or to require mouse movement that is extremely delicate or rapid.