Pet and Underworld Hall of Fame are stagnant and mostly won't change much.
The most broken is Underworld since you can't really even catch up... never.
Since you don't have much options to change your position it wouldn't be too exciting. Just a "win more" system.
Now if we would get some weekly or monthly events / Halls of Fame with rewards, that would be cool.
Although there's no system to send out these rewards