You "can" fly with a mouse. You "can" also amputate your own leg and get around on crutches.
There is no substitute for a joystick.
Given equal skills (saying you cloned the exact pilot) the pilot with the joystick will own the pilot with the mouse.
The reason you hear of these great sticks flying with a mouse is because they are great sticks. The skill level overcomes the skill level of their opponents. Put them on joysticks and they would be more potent.
Mouse control limits your abilities, limits your input controls.
That's my opinion, and I know it's shared by many others also.