Given Trek's lackluster record with sex in movies (Uhura and Spock bickering like idiots while they're about to be shot out of the air; Carol Marcus's awkward underwear scene; Kirk being a one-dimensional lothario complete with twin space-kitty babes), and given other sci-fi's advances in it (nuBSG; hell, Starship Troopers), maybe Ilia could come in as an elegant, unnervingly attractive, and thematically-rich character.
Chekov became chief engineer on Starship after only a year of service so a promotion to a new ship in a more senior position to navigator makes a lot of sense.
My personal view overall is that Rand should have been in the movies, starting as Pike's yeoman, from the beginning, as a more security-trained supporting character like Keenser or Cupcake, rather than leaving her out altogether. She would not need many lines but would be a female presence - she could have helped subdue Kirk in ST09 or been part of the shuttle crew in STID (although why you would take your secretary on that kind of mission is a bit of a stretch).
Three movies in and still no Rand. Chapel was written out unceremoniously, and the timing coming just after Majel's passing really grated on me. Alice Eve has not returned for this movie, making her effectively a guest star. They need more recurring female characters and I'd prefer to see them reboot and update the existing ones than start fresh.
Bringing in Ilia is a logical step at navigation and improves the female dynamic while at the same time leaving scope for the juvenile humour - Deltans have no sexual hang ups so why would Ilia worry about stripping to her underwear? She could potentially turn the tables on Kirk in that regard.
I don't favour the focus of her character being on sexuality but as far as the NuTrek writers go, they could be snickering behind their hands for hours (not a euphemism). It's a plus for them. Further, her empathic abilities are nebulous enough to be interesting and not plot busting like Troi - they appear to be pheromone based rather than telepathic (although Deltan's do seem to have telepathic links to other Deltans in the novels at least). Actually having a scientific basis for the abilities can lead to interesting story ideas (using her own pheromones to affect someone else's brain chemistry is something we saw in TMP for example).
Finally, if they left Chekov out in the fourth movie and brought in his younger brother in the fifth, Trekkies would understand that this is the REAL Chekov Prime. It remains respectful to Yelchin's contribution while pandering to nerd-ragers like me who were irritated at them shoe-horning in a character as a name-check in favour of other (notably female) characters that would have been as effective and the correct age to appear.
I have thoroughly enjoyed Yelchin's contribution and his death is a terrible tragedy. I don't think his contribution would be diminished by recasting but nor do I think Chekov is so vital that recasting is necessary. I'd rather Yelchin's Chekov lived on albeit off camera.