Dick debatably has enough on his plate (and trying to restrain his own impulses) without needing to deal with Jason’s violent tendencies, and would Batman really just be cool with Jason hanging out far from Gotham on a regular basis?
There’s also the question of Jason being allowed to ditch Gotham to hang with his Bat-bro.
Well, if Jason is around more often because he joins the team, then even diehard comics fans can’t predict what’s going to happen based on canon.