I don't know how a virtual pilot base would work, but here at DAL, the virtual FAs bases make it seem like a bad idea. The FAs based in Florida say that there are no reserves: if you get sick or whatever, you have to find your own replacement. The limited size of the bases make them very senior, with almost no movement. Also, FAs can fly any airplane that transits the base, while we cannot. Thus, it limits marketing's ability to change aircraft month-to-month. So, there are costs to closing a base if they decided the aircraft isn't serving that city enough to have a virtual base (costs like training, moving, etc).
Personally, I don't see virtual pilot bases as useful to us or the company. Our contract requires certain time off in base that you don't have to have on a overnight. Second, we already have "Regional" chief pilot offices, so there isn't the cost of a full base anymore.