Why not necessary to discharge a monitor high voltage compare to a television?
If you compare a television and a monitor flyback transformer, you will observe that the monitor flyback have an internal high voltage film capacitor built into it. Generally, television flyback do not have this internal capacitor. The value of the internal capacitor is usually between 1.5 nanofarad to 4.5 nanofarad with a working voltage of 30 to 35 kilovolt. You can check the capacitance value using a digital capacitance meter. The voltage can be dangerous if you did not discharge it in a proper way.
A flyback transformer schematic will reveal the differences between a tv and a monitor flyback. If you look at the tv flyback schematic, the divider (for screen and focus) are tapped from the middle winding before the output diode. Due to this design, when a tv is switch off the high voltage from the picture tube (infact picture tube is a large capacitor)
can't be discharge because of the output diode preventing the current from flowing to the divider. Thus the high voltage remain in the tube and can only be discharge with a screw driver connect between the cold ground and the flyback anode. You will hear arcing sound from the spark generated when discharging the high voltage.
As for a monitor flyback transformer, the divider are located after the output diode where when the monitor is switched off, the divider (with a high resistance-more than a hundred megaohm) will discharge the high voltage capacitor almost instantly. Thus there is no need to discharge a monitor when you want to work on it. However for safety purposes, i strongly suggest to those who are new in the monitor and tv repair field to discharge the high voltage before start servicing the equipments. For your information the divider in the monitor became defective much faster(due to heat) than a television because it tapped from a 24 kilovolt source compare to tv which tapped from a 8 kilovolt source. A defective divider can be solve using a monitor blur buster.