I don’t know about your impression of the Old Testament prophets, but to me they seem to be more like John the Baptist who wore a “garment of camel’s hair and a leather belt around his waist, and his food was locusts and wild honey”. And he preached in the wilderness. (Matthew 3:1-4) Or take Elijah who when threatened by Jezebel felt safer escaping to the wilderness (1 Kings 19:8). But in reading the Old Testament, this view is not always accurate. Some of them were very well connected.
Elisha evidently had a considerable amount of influence over other prophets. 2 Kings 6 tells us the sons of the prophets asked Elisha for permission to build a new residence for themselves.
Elisha evidently was well traveled. The Shunammite woman built him a room where Elisha could stay whenever he passed that way.
Elijah was known throughout the region of Israel because he anointed the king of Syria (1 Kings 19). Elisha was also known by the king of Syria who asked him if he would recover from an illness (2 Kings 8:7-9).
When Naaman came to Israel to be cured of his leprosy, the king of Israel tore his clothes because he thought the king of Syria was sending Naaman to start a quarrel with him (2 Kings 5). How did Elisha hear the king of Israel tore his clothes unless he was well connected to what happened in the palace?
Even Elisha’s servant talked to the king of Israel about the deeds of Elisha 2 Kings 8). One does not gossip with the king unless there is some close connection there.
On second thought, that the Old Testament prophets were well connected should not be a surprise. To influence a society, we must participate in that society.
