I'm in the large chunk of audience that really didn't dig Palmer's disrespectful (intended or otherwise) rapport with Chief in Halo 4- her character has been battling that bad first impression for me ever since, and its sour taste is still lingering.
She picked up with John like she was as old and as dear a friend as Johnson had been in the original trilogy; only, Johnson and Chief had history hinted at even in those games-- Troy Denning's Master Chief books have done a phenomenal job of fleshing out and detailing that history dating all the way back to their first meeting when John was just a teenager and Avery was a grizzled veteran. Palmer, on the other hand, while having served as an ODST during the H/C War (Matt Forbeck gives us some tantalizing insight into her career as a Helljumper in his "Blood" books) had only been a "peacetime" Spartan and had never met John before when she treated him with such depricating familiarity. She seemed more in-line with Del Rio's assessment that Chief was an aging relic of an old war than Lasky's awe and appreciation of John as humanity's greatest champion. It wasn't a great move to endear her to a lot of the classic audience.
Anyways, while I stand by all of those opinions, I do believe that Palmer, like most of the Reclaimer Saga cast, deserves to have more time and attention for development. I'm not in the camp of "Kill off all the Spartans on Infinity and all of Fireteam Osiris," because I don't think that accomplishes much of anything and in fact just makes Halo 4 and 5 into complete wastes instead of carrying forward redeeming elements from them and polishing them on into the future.
Do I think Palmer should have a big role in Infinite? No. But I do think she has a place and it would be very nice to see some development for her character, especially in a challenging situation like The Banished are seeming to provide on Zeta Halo.