You just don't have very good hand-eye coordination then. It's not really that hard to adapt to using a mouse. Add to that a mouse can allow you to shoot at specific body-parts instead of madly hoping to hit the enemy at all, and the mouse is totally superior. My first time playing an FPS...
You're right on most of the points but this. You don't see an auto-aim feature for the vast majority of PC games. You just can't accurately use a gamepad without said auto-aim.