When backpacking or hiking, the only time I have ever needed to split a stick of wood was to get to the dry inside to get a fire going. If easy to burn ground wood is not available when backpacking, I just do without the fire anyway. So many wildernesses and parks are beginning to ban fires, especially when fire danger starts to mount that a campfire is purely for aethestic reasons for us.
In campgrounds or hunting camps, an axe is always at hand. In fact, many western forests require a bucket, shovel and axe in every vehicle.