Isn’t the lack of correspondence between Otto and Ormund a little odd?

Wasn’t Otto a tool of the Hightowers? Actively working to promote his family’s interests at court? I find it odd that the Lord of Oldtown wouldn’t want to correspond with the Hand of the King, no matter his personal disdain for House Targaryen, Otto was the most powerful man in the realm after the king himself and effectively ruled the Seven Kingdoms alongside Alicent during Visery’s later years.