I'm not sure if I fully understand your problem, but one of the main tenets of creating good design is redundancy and accessibility.
Creating multiple paths to the same solution accounts for a wider audience, and caters to personal preference. In your example, not everyone knows about the
F4 shortcut, hence the
Exit button is the only way.
You can look at the Instagram app or Music Apps as an example. You can double tap an image, or click on the heart icon; you can press
Next or swipe to the next song.
People have different needs, tools, and hardware. By providing solutions that utilize different input methods, you are creating a more accessible environment. In your example, is a keyboard/mouse is a common hardware configuration, but what about users that only use a mouse? Or only a keyboard? Or a touch screen? Or voice-input commands?