When you hold a pencil, the tip is close to your finger tips and it's very easy to discern where to tip is intuitively. The biggest reason using the mouse works so horribly isn't due to having to grip a huge object, it's simply because the point of reference is unintuitive. Case example for this is using a pencil vs using a mouse to write in paint.

Being forced to used the center of your knuckles (that's the part of your body that most often lines up with sensor) as your point of reference robs you of the natural precision of your fingertips.

But that's not all, the dominant part of your body when it comes to being able to make precise movements down to the millimeter are your finger tips. That will make your aim inconsistent if you're using the entire mouse as your point of reference. The thing that factors the most into this is something I'll call arcing, unless you're able to keep your mouse at the exact same angle relative to your desk (which is impossible), there will be discrepancies in how much distance different points on the mouse has traveled. You need to be aware of the exact position of the sensor to maximize the precision of your aim. But there's so much at play here, the mouse is a relatively big object compared to the sensor and the precision you're asking from it, trying to think of the entire mouse as the point of reference for your crosshair movement is like trying to press small buttons with big fingers. Most people just pick up the mouse and use it at that's the end of it, sorta 'I move left, crosshair moves left, practice makes perfect'. Why is the sensor always in the dead center? It's so unintuitive and a pain to constantly keep yourself aware of the sensor's position to maximize your aiming accuracy. The main thing I keep coming back to is my mouse, not specifically 'my' mouse but all mouses in general. As a competitive gamer by profession (in FPSs), I've been thinking a lot about what could be improved in my peripherals.

Snagit 2018 not capturing mouse