I think one of the biggest wasted potentials with Jean Grey was having her not join Captain America and the Avengers as the Phoenix after she was brought back to life during 'Phoenix Resurrection'. They brought her back and then sent the Phoenix Force away. I would have kept the Phoenix Force with Jean and have her decide to keep away from the X-Men for a while; what with Cyclops being dead, and finding out that he was treated so poorly by their family. She forgave everyone far too quickly in my opinion, especially the inhumans and Black Bolt.
This could've led Jean to joining the Avengers and as their story progressed together she could have confronted her teammates one by one, talking about the 'Avengers vs. X-Men' situation—which involved the Phoenix Force that's part of her—their failure to assist the mutants of the world, and their treatment of her husband. She could've done this all while working as an Avenger.
The most compelling interactions would've been with Steve Rogers, Captain America. Thus leading to a romance between Jean Grey and Cap!
I think that could've made for a better use of Jean than 'X-Men: Red'. She could've grown much more realistically and they could have not only explored the Avengers' stance on mutants and mutant problems, but also cleaned up the mess that was 'Avengers vs. X-Men' retroactively, do some character deep dives, and even have Jean be questioned of her place among mutants as the Avengers point out her cosmic place in the universe. Sort of like an 'Avatar: The Last Airbender' situation where Aang is an air nomad, but his duties as the Avatar trump his desires as a monk. The Avengers could point out that while Jean was born a mutant, the Phoenix Force made her a part of the cosmic landscape, making her responsibilities be to all the people in the universe, not just mutants.
I don't know, just some dumb stuff I think about. All of this while she locks lips with Cap, of course!