The 104 keys on a full-size layout provide a huge selection of potential inputs, and mapping game functions across those readily accessible keys gives developers and players a huge amount of flexibility in how they want to control their experience.
The primary advantage mice have over controllers is the precision they allow when aiming, as well as the range of movement provided by the additional surface area of the mousepad. This means potentially faster movement
In a first person shooter, or any game where accuracy is important, a mouse is usually a competitive advantage, and facilitates easier execution of reaction-based shooting, like flickshots. This advantage is significant enough that controller-based FPS will sometimes implement aim assist, which is designed to mitigate that inherent disadvantage.
Mice, like keyboards, vary widely in functionality and design, including features like modular design, customizable buttons, and a huge selection of options for just about every type of gamer.
Analog joysticks may lack the precision and speed of a mouse, but if you press forward slightly the character might walk, and if you push harder, they might run. Holding a pressure-sensitive button moves your vehicle forward slowly; pressing all the way down could fully engage the throttle. These contextually sensitive buttons can provide a steadiness of movement that a keyboard might not be able to achieve. A joystick also makes continuous motion, like the panning of a camera for example, more consistent.