Also I'm not sure what you're talking about when you say using a controller has a more realistic and immersive feel. When I play an FPS with a keyboard and mouse it's almost like I'm holding a gun with my mouse hand, when using a controller it just feels like I'm simply moving a crosshair around the screen with a joystick.
Using a controller is reasonably close to what its like holding a handgun/pistol.
Holding a mouse is nothing like firing any handgun, rifle or shotgun I've ever used, heck my mouse doesn't even have rumble to simulate recoil.