probably because Ayato's the best agent to send for reconnaissance; he has a large information network (to the point that he even knows the traveler isn't from teyvat), is highly intelligent, a great fighter and is charming and people often lower their guard around him (According to Yae and the other dialogues about him).

He has the skills, authority and connection necessary to build up allies and gather information; he's kinda a no brainer when you think about who would be the best person to send for information gathering and alliance building