Why is this multimeter power supply short circuit when off
I realised something that may reveal the answer after I turned the device off and watched the LCD.

When a segment of the LCD is activated, if the pin that controls it is then allowed to float (because the device is turned off) the LCD takes a little while to fade. If however the common pin and the segment pins are shorted together, the LCD turns off much faster.

So far my best theory is therefore that short circuiting the LCD driver chips when the power is turned off is to provide the appearance of switching off quickly rather than fading slowly.