It used to be standard practice / teaching instruction in Scotland that after awarding a penalty the referee should run towards the goal line towards where the penalty area line intersects. If you watch old video footage of matches from the 80s and 90s this was the standard procedure.
The thinking behind it was to create distance between the referee and any potentially aggrieved defenders, and the goal line essentially became a barrier that players shouldn't cross. It also meant that if any player decided to protest, they were running a fair distance to do so, and it became a very easy caution for dissent that no fair minded person could argue with.
As far as I am aware it was never official advice to caution for leaving the field of play, but in the 90s there were apocryphal tales of certain grassroots referees doing so and adding in a dissent caution as well meaning that the player would be sent off.
