To be blunt, it's not the filmmakers' job to "pay homage" to any given actor, no matter how important she was to the past franchise. It's their job to tell a story that works in and of itself rather than just as an exercise in nostalgia. And that means using characters in ways that serve a purpose in the story. Movies don't have as much room as series TV to flesh out supporting characters, so they have to limit themselves to the supporting characters that contribute something useful.
And let's face it, our feelings about the actress aside, Chapel's importance as a character isn't all that great. The only thing that ever really defined her aside from her job as nurse was her crush on Spock, which doesn't fit into the new paradigm with Spock in a relationship with Uhura. She was in fewer than 1/3 of the series' episodes and never played a major role in the movies except maybe in TMP. The fact is, she's expendable. At least they mentioned her, which is something.
I don't agree fully. Trek has fallen into that pit too often in all the franchises. Why was Chekov promoted to chief engineer if it wasn't a poorly thought out attempt to pay homage to the character? Why use McCoy instead of Cupcake (or Chekov for that matter since he is reasonably qualified) to work on a bomb if it wasn't an homage to the character from one of the sillier moments in STVI? There were plenty of other ways they could have used the characters that made more sense. They are incredibly indulgent with these characters all the time even where it doesn't really work in the story (unless you're 12).
There were lots of nameless supporting characters in the movie any one of whom could have been tweaked with minimal effort to represent pre-existing characters.
And Christopher, you pay homage to supporting characters all the time in your novels even where doing so is not important to the plot! It's one of the things I admire
It is true to say that Chapel falls off the edge of the recurring characters because she rarely left the ship and did little overall (except save Spock's life once) but she appeared in almost as many episodes as Chekov, and they went out of their way to include him and to give him things to do that were never really part of his TOS character. Why is it so justifiable for Chekov but wrong to update Chapel to hand out more than hyposprays and moon over a man? I think you guys are justifying a double standard.
Since they decided to keep her as a nurse instead of a scientist, I can understand why they couldn't give her a major role (although as I say, the tribble research would have been perfectly in character). I stand by what I said. Writing her out completely is disrespectful to the actress and the character and to the women in the franchise generally.