Challenge logs are designed for the experience points, the gil is just an added bonus for those who are already 50.

The reason why Hunts are not part of the challenge log is because the content itself is designated for after you are 50, so for now it wouldn't really be logical to add a challenge log for Hunts since the challenge logs main aspect is extra xp boost. However when 3.0 comes around they may consider adding Hunts to the challenge log since the cap will be going up 10 levels and the ability to add an xp bonus to the hunt challenge logs would be possible.