Given NYC's sky-high rent, I wonder what would happen to the real estate market if these apartments were occupied by full-time residents. It seems grossly inefficient to have an apartment sitting empty for that long, no matter how much money you have. I guess there aren't too many good options, since airbnb-style renting is probably a) illegal and b) frowned upon by the building. If I were these people, I'd just treat the apartment as an investment property and stay in a really nice hotel when I was in town.
If you really where those people, it would be too much of a burden and hassle to have to deal with it as an investment property. They just don't want to deal with booking hotel rooms, the hassles. They can store whatever and know that it will remain untouched, they can fly into town and have an affair and leave, and best of all, it's prime real estate that figure will stay in high demand for the foreseeable future.
That was my take-away as well. In addition to having a relatively stable investment (prime real estate in a popular city should hold value very well), you get to avoid the hassle of booking travel, and can manage your expectations about what you're getting. It's a more exclusive and more-personal place to visit or rest than a hotel, since it can have YOUR art, YOUR bathrobe, etc.