I think that you are being too hard on Matt. He is shell-shocked at the moment, being in love for the first time, finding out that he has become a noble of all things.

Also he has not always been just a whiny boy doing heroic deeds because he was taveran. He carried Elayne's letter to her mother and delivered it despite the difficulties. He went to Tear to find the girls because he found out that Elayne was in danger, and he rescued them. He sees it as his responsibility to help Elayne and Nyn in Ebou Dar, no matter how difficult the girls make it. Being Taverran put him in situations where he had to fight bu t when he does he looks after his men.

I think that it is taverran that is pulling him to Caemlyn before rescuing Moirraine. Perhaps he needs info from Perrin re Slayer entering TOG. or perhaps Verin's letter has info he needs.

I like Matt. He may be a rascal but he has a good heart.