The reason for writing shorthand of noble gases’ electron configurations is because it is a more effective way to communicate the structure of these gasses. If the entire electron configuration was written out, it’d be rather lengthy and more confusing since the noble gasses are positioned all the way across the periodic table of the elements on the right. They would also be repetitive. Since all noble gasses do not bond because they satisfy the octet rule, they can all be written in the same way, just changing the symbol for what gas you are speaking of. This makes understanding the electron configuration of the noble gasses much quicker and easier.
I hope this helps! :)