What is the reason for differentiating the time of the restricted Takbir on Eid al-Adha between non-muhrim and muhrim?

Some scholars differentiated between the pilgrim (muhrim) and non-pilgrim concerning the restricted takbir. The non-pilgrim begins the takbir from the dawn of the Day of Arafah, while the pilgrim begins it from the Dhuhr of the Day of Sacrifice, due to being occupied with the talbiyah (definition) before that, which is legislated after every obligatory prayer. The jurists are of the opinion that the talbiyah is a form of remembrance legislated after obligatory prayers, and it continues until after the stoning of Jamrat al-Aqabah. Once the talbiyah ends, the pilgrim begins the restricted takbir.