Why is there open/deadspace under most wooden furniture
The main reason is that woodworking of old days, Joinery was more of an art than a mechanised given. The structure was designed to accommodate for wood settling and fluctuating due to weather conditions (humidity etc) ... 

Basically, the most stable structure was one, where the weight rested on the four points which were the most stable (the legs or balls) As Rozwel noted, a flat board on the floor would be susceptible to high points which would unsettle the joinery of the piece as the wood base would most certainly flex to accommodate for the high point and in doing so, throw the piece out of square.

Short answer, the four contact points would lead to a more stable cabinet over a more diverse set of floor types.