Basically, it is Marvel, the company, not Morrison, who will dicate who is the Phoenix.

Marvel has made all versions of Jean Grey the Phoenix. New X-Men, Ultimate X-Men, TAS X-Men, X2 X-Men, and now Evolution X-Men.

The X-Men got turned back into a school because of the movie. While Claremont wanted Cyclops to stay dead, he couldn't the Marvel corporation decided, because of the movie.

Rachel won't be used, because most fans know Jean Grey as the Phoenix.

Also, Claremont did not even try to have Rachel in X-Treme. She has been banished. Instead, he would have Jean guest star.