There was a comment way above that it would be hard to run a company while choreographing new work. That HAS been done -- think Balanchine, Ashton (not to mention Bournonville and Petipa, and every great modern dancer you can think of). But it does seem early to speculate.
Very true, but as you've pointed out yourself elsewhere, it's a complex bag of tricks, running a ballet company. If you look at the modern dance model (and in many ways Balanchine fits into this category), the company is primarily a vehicle for one person's artistic output -- it's their aesthetic, their outlet. It exists to serve their creative work.
(yes I know that Balanchine shared his theater with other choreographers, some of them much more "I" oriented than he was himself, but really -- it was Balanchine's company)
(and yes, this makes for a new batch of challenges when the choreographer/director dies/moves on -- we've seen this happen in the far and recent past, and we'll see plenty more in the future)
I don't know enough about the workings of the Danish company during Bournonville's life to say much concretely about his administration. And Petipa was a part of an organization so Byzantine I'm not sure we can really compare it to current ballet companies. But I know that for most of his creative life, Ashton was not the director of the Sadler's Wells/Royal Ballet, and there's certainly a chunk of discussion about his tenure as AD that implies he wasn't an especially great manager.
What we do get, frequently, are artistic directors who are choreographers in the same way that I'm a chef -- I make no pretense to really high-end cooking, but I get dinner on the table most nights in our house. Many companies have director/choreographers who can fill in the blanks of the season, depending on what other works they've got programmed. Kent Stowell at Pacific Northwest Ballet made an incredibly wide variety of works during his 30 year tenure. Some of them were excellent whatever the criteria, most of them were works "d'occasion" that were tailored to the situation at hand, giving particular dancers the challenge they needed or filling a certain niche in the repertory. The company could not have grown as it did without that kind of in-house talent -- he was exactly what they needed.
(to add an extra twist, Stowell is an excellent cook, while his son Ethan is a renown chef/restauranteur)
ABT has a substantial repertory -- while they will always need to make room for new work, I don't know that they need to be run by a choreographer.