I feel like all items with sentimental value should level up with the character. I mean there has been a bunch, Bianca, Asala, Duncan's shield, zevrans dalish gloves and howes bow... I always feel weird about selling them if I get something better.
Also Sten says that Asala was given to him the day he joined the berasaad. So I think the day he became "Sten" that's when he got Asala. So when he becomes "Arishok" he may view it as getting a new role, a new weapon and a new life and soul. Just a thought....
I'm this way as well, I never took Asala away from Sten after he reclaimed it and while I took away Wesley's Shield from Aveline, I always put it in storage because I just couldn't see those characters parting from them just for the sake of inventory space.
In a general sense though I just can't see Varric using anything other than a crossbow, I feel it would go against his character from what we saw in Dragon Age 2. He doesn't seem the agile type, and longbows involve a completely different discipline from crossbows. Whereas characters like Sera and Cole are blank slates that are being written to envelop both weapon styles.