Touch screen is a known issue on G2. I experienced "fix" by flashing some custom Rom and kernel. I believe different voltage control to the touch panel will have different result. I'm now totally out of touch screen problem after flashing custom Rom and kernel.
Another thing is sensitivity. Sensitivity on G2 Touch panel is poor. I used to use tempered glass but found that made difficulty for the panel to response. I got everything fix now without any screen protector.