The issue is primarily with any bacteria in the food being able to multiply between 40F and 140F. So just not having eggs or milk doesn’t mean that it’s sterile enough to not need to follow the food safety requirements.

Once you open the can or container of cookie dough it’s certainly not sterile anymore and no longer able to be keep at room temperature without possibility of bacteria growing, so even if it was stored in a sterile environment once it’s on the sheet it isn’t shelf stable anymore.