If the portraits for the Order are painted on ivory, and if there is a stash already prepared that would be used for Kate's, and if HM is not prepared to have a new one made for her on another medium, I believe it is likely that it is the reason Kate doesn't have one. Or, if she has one, chooses not to wear it.
Kate has popped out the heir and the spare for that generation, and, apart from some issues about skirts and weather conditions, and necklines, I don't think Kate has done anything to frighten the Queen's horses.
No, I think the absence of the yellow ribbon on the red dress at the state banquet is likely to be the ivory, and in particular William's call for Buckingham Palace's collection of ivory, including valuable artwork, to be destroyed. That apparently includes a miniature portrait of HM as a toddler painted in 1928, and HM might be rather fond of it and not want it destroyed. Or the numerous other ivory items in the collection.
A man who wants his grandmother to destroy all the Royal collection of ivoryware is not going to want her to give his wife an ivory brooch, and I doubt he would refrain from expressing his opinion on the subject. I understand Kate has equally strong views on the subject. She would actually go up in my estimation if it turned out she had been given one but refuses to wear it. Such a shame we'll probably never know. If she is seen sporting one at some future date, I'm willing to bet it won't be made of ivory.