Bad monitors are just a gimped setup. Ungimping your setup doesn't mean compensating for a lack of skill. 60Hz LCDs are extremely hard on the eyes because of the large amount of motion blur inherent to displaying something at 60Hz without strobing. They also had very bad pixel response in 1999. They also had medium-high input lag depending on the model and what colors are being displayed on the screen. You also wanted a high end CRT for both better still image sharpness and better refresh rate (lots of them only did 60Hz or 75Hz, and anything that maxed out at 75Hz probably had bad focus, because focus decreases as you raise the refresh rate). Once you start fixing your system (changing mouse polling rate from 125Hz, disabling mouse acceleration), the monitor is just one more thing to fix. All of this is needed just to be able to game competently with the top say, 50% of players (unless your play style just avoids aiming).
I remember in UT99 for years always running into situations where my aim was slightly off in situations where I was dead sure it should have hit. Turns out it just used the mouse acceleration feature in windows: the speed at which you move the mouse influences how far the crosshair (or cursor) moves. Once I disabled that I became about 5x better. The next big jumps were turning off vsync (and making sure it doesn't turn itself back on) and going back to CRT from LCD.
I remember in UT99 for years always running into situations where my aim was slightly off in situations where I was dead sure it should have hit. Turns out it just used the mouse acceleration feature in windows: the speed at which you move the mouse influences how far the crosshair (or cursor) moves. Once I disabled that I became about 5x better. The next big jumps were turning off vsync (and making sure it doesn't turn itself back on) and going back to CRT from LCD.