Does City Ballet try to keep a fixed number of dancers on their roster or does the number vary? Is the number of new dancers that that they hire as apprentices each year, based on the number of people that retire from the ranks of the corps de ballet or the number that retire from the entire company?
Since city ballet has such vast Balanchine and Robbins repertoire, why do they need ANY outside choreography? If they danced nothing but Balanchine and Robbins they couldn't go for years and never repeat themselves?
Does the the core City Ballet audience really want to see other works?
Sort of off the original topic but...
NYCB has always been committed to dancing premiers and even when Balanchine and Robbins were alive danced works by other choreographers--some of substance, many...not so much. Their core audience? If, as a onetime New Yorker, now non-New Yorker who comes to NY periodically to see NYCB I count as core audience, then I can answer that I certainly think the commitment to new work matters.
As a result of the company's commitment a number of major new works including works by Wheeldon and Ratmansky have premiered there, as well as works by choreographers such as Preljocaj, Bigonzetti, and Forsythe that I at least don't find a waste of time. (Balanchine's ballets are, of course, incomparable and the basis as they should be of the repertory.) As you probably know several critics have started championing Justin Peck in the last year. Peck and Wheeldon really emerged through NYCB and Ratmansky's career took a great leap forward with the creation of Russian Seasons for the company...Namouna which is arguably his best ballet was created for them. These works contribute to NYCB, but also to ballet as an art form. (I would rather see Namouna a third time than, say, Robbins' I'm Old Fashioned.)
The importance of new works in developing dancers has often been debated on this website--indeed the whole issue you raise about repertory has been taken up, and a lot of different perspectives expressed...but for myself, I think it wouldn't be NYCB if it were simply filling a curatorial function even if that is the company's most important function.
The dancer numbers have grown and contracted over the span of years (recently contracting after the 2008 financial crisis for example), but within any short period of time the numbers are I believe usually pretty steady and retirements/departures do impact the numbers of new dancers they can accept or promote. Others, who follow the day to day workings of the company more closely than I, can comment in more detail on that.
More related to topic (though not to the larger structural issues): Perhaps I missed it, but I don't recall that Gen Horiuchi has been mentioned. He came to NYCB in the early 80's (Wikipedia says invited by Balanchine) and was frequently featured by Peter Martins, who created roles for him--actually one of the more prominent dancers of the early Martins era.