I'd leave the hunting log alone or find some other reason to complete it (like job specific gear).

The point of the hunting log, back in early ARR, was that it provided a way to gain experience back when there were less options for gaining experience. If I recall, leveling roulette wasn't released until later in the ARR patch cycle. Dungeon experience was pretty bad as well, initially. People just farmed FATEs for experience. And early on, FATEs didn't adjust to the server population in the zone. So, if you weren't an AOE range job, your ability to get experience on physical damage jobs that couldn't gap-close was fairly limited.

Once leveling roulette came out and dungeon experience was upped, the only point of the hunting log was to get a job to 15 so they could run dungeons for better experience.

With there being a plethora of ways to gain experience now, the current role of the hunting log is moot.