Vacuum Fluorescent Display: What are the benefits of an AC filament driver instead of DC?
The filament is also the cathode of the device.
With DC excitation one end has essentially a different DC bias voltage than the other and will result in different emission. This may give uneven illumination or wear out characteristics than when using AC which evens out the bias.
As other posters have commented it is also preferable to provide the DC bias relative to the center tap of the filament or to have a center-tapped AC supply.