FPS Games, Recoil and Spread

So, in FPS games, there are a number of things at work that determine your accuracy, as you know.

Excuse me if these terms are something you already know.

Recoil is something you have to adjust for based on the power and rate of fire for the weapon. High power weapons usually have high recoil to reduce the time between shots that they are fired. A high rate of fire weapon has high recoil because each projectile knocks the weapon in a certain direction.

Spread is used to emulate stability of your aim. If you are running, the spread is very high, if you are walking it is low, if you are crouching it is even less and if you are prone and not moving at all it is at its lowest.

This isn't an original idea at all, but wouldn't it provide a better gameplay experience if the concept of spread was replaced with the crosshair moving around? So, if you are moving or stationary, standing straight up, crouching, prone, whatever the crosshair would be the same size. However, to do the same thing that spread does, the crosshair would move around. If you are walking at high speed the crosshair would be moving up and down, left and right. Whereever it was is where the projectile would go, and there would be no randomness or misunderstandings about where you were actually aiming. Like recoil, this would be something that the user could control more directly. With recoil you can compensate somewhat for it if you know how. With spread you can only compensate for it indirectly by reducing the randomness. With a moving crosshair, you would be able to adjust your aim to compensate for your stance or movement speed if you knew how, and there would be no "what? I had the crosshair centered on the other player, what happened?" kind of reactions.

Note: It seems like some games, e.g. Battlefield 4, have scope sway, which is similar to this, but the scope sway is present along with spread. Also, for games where there is no crosshair or it can be disabled, the rendering of the weapon would have to realistically show that is was bobbing, which it seems to do in a fair amount of games already.

Thoughts? Comments? The only thing I can think of that might make this an issue is that having a moving object that the player constantly needs to track might be annoying or headache inducing for some, similar to motion blur effects.