I'm only discussing PvE, although some of this might apply elsewhere.
Elite specializations have has one significant issue across the board: they reduce the ability to play the core profession. Elites beef up the character too much to ignore. It simply makes playing a core profession undesirable.
To fix this, I think the core specializations should have the ability to be slotted as an elite, and receive a corresponding increase in power to match.
I'm not sure how much more powerful a current elite spec is compared to non-elite ones, but devs must have access to that information. So, if they do, that would make it nearly trivial to do the calculations: just multiply by that percentage.
Getting them to be slotted as elite might be more complicated, though. Perhaps creating a new trait line with the same traits, but a different name might work. Then, disallow using the old and the new together.
I would really like to be able to play a guardian healer as a guardian, but having druids in the game makes that a stripped-down option. Same thing for warriors, necros, and most of the professions.