What is the wisdom behind the the Prophet (ﷺ) vocalizing the intention for Hajj, even though vocalizing the intention is not permissible?

We have not come across any statement prohibiting the utterance of the intention (niyyah) in acts of worship. The wisdom behind the permissibility for a Hajj or Umrah pilgrim to utter what he has entered into ihram for is to distinguish between the rituals, due to the difference in their rulings. Al-Buhuti said: "It is recommended to utter what one has entered into ihram for, so that he intends a specific ritual, due to the action of the Prophet (peace be upon him) and those with him during the Farewell Pilgrimage, and because the rulings for that differ, so it is recommended to specify it so that its requirements may follow."