Whether or not to add salt to an omelette is a matter of personal preference. Salt can enhance the flavors of the ingredients and help bring out the taste of the dish. Many people do add a pinch of salt to their omelettes to season them.
However, some ingredients commonly used in omelettes, like cheese, ham, or bacon, can be salty on their own. If you're using these ingredients, you might want to taste the omelette first before adding additional salt. Also, some people may be on a low-sodium diet or prefer to limit their salt intake for health reasons, in which case they may choose to omit or reduce the amount of salt added to their omelette.
In summary, it's a personal choice whether to add salt to an omelette. It's a good idea to taste and adjust the seasoning according to your preference and dietary needs.