They really just don't like him, and I think they undermine their own favorites a lot by needing to crib stuff from Hal. I think all the GLs have their own stuff that can be adapted or are versatile enough that they can come up with new ideas for them.
The general GL mythos can be adapted around any character and it can work. But yeah, stuff like Abin Sur being used for DCAU Kyle instead of just crafting another origin episode for Kyle is pretty grating. Though in fairness to Timm and co, I think they wanted to use Hal but DC made them use Kyle to stay consistent with current comics. This is why Kyle had brown hair in the show and it's similar to Jason being named "Tim" over in TNBA