That's impossible, if you change your movement it will mispredict and thus cause more lag, while exactly when you change is when it should feel the best. Consistency feels better.
Just like no magic gizmo can reduce audio lag other than have actual proper low latency standards (for bluetooth audio): it can never predict when you will hit the button to fire your weapon, etc..., in games
It will not cause more lag, it will just not be accurate to where your cursor actually should be when the frame gets displayed. For people with strong computers you would only need to predict a few ms forward in time which should be possible to get really accurate.
>it can never predict when you will hit the button to fire your weapon
That is not what is happening. What is happening is that time between registering the click and the frame being displayed. The prediction I'm talking about would be predicting subframe mouse movements. This behaviour is more for smooth mouse look. For shooting you want to have a precise timestamp of when the click happened so that you can see if at that moment in time the shot would have hit. The position where you are looking when shooting and the position where you are looking on screen are different things.
No, Nvidia Reflex is a step in the right direction. You want to sample input at the latest possible time and then create a frame for that input. Sampling input at the beginning of a frame is the worst time you can choose as that will guarantee at least a frame of latency. If you are able to render in 20% of the time of a frame you want to sample the input and then start rendering 80% of the way through the current frame that way you are only add 20% of a frame of latency at a minimum in this part of the system.
This is how things are done in VR, but the location of input devices are also exterpolated to predict where they should be located at time they will be displayed.