Why is via fencing not used to cover the whole PCB?
Because a via fence also requires continuity across a large area of the board on at least the top and ground plain, it's difficult to route signals through a via fence, so its probably not wise to cover the entire board with it. Cost is usually not an issue unless dealing in large quantities. 

Via fences will provide capacitance to ground, so that would be the main advantage\disadvantage.