Frank,
OK, I am not up with the RA Aus situation; correct me if I'm wrong, RA Aus cannot access C or D? If that is the case, from a safety point of view they probably shouldn't be allowed into E where the only separation tool is radio, where the RA Aus pilots are expected to listen and determine whether I am a threat?
Whatever they don't have (experience?) that stops them operating in D or C would, I expect, also preclude them from E, given that it is more demanding on the VFR operationally. In D or C, they (us as well) just get told what to do. Easy.
Re Alice specifically, if ATC won't let them thru, chances are it's because there's too much heavy metal in the way, and Class E won't remove that heavy metal, it just makes it less visible (until it hits you).