Very true. I confess that a saw just does it for me. I’ve worked with both saws and axes from a young age and have never had an accident with a saw. I cannot say the same about an axe, or even a knife. Here are the benefits I have seen of a good folding saw (6”-9”):

• The folding saw is as quick, or quicker than a chopper or smaller camp axe for cutting through green or hard wood up to 4 inches. This makes it perfect for general woodcraft, constructing shelters and traps or preparing firewood.
  It is far lighter than either a large knife or axe when backpacking or hiking.
  It is more inconspicuous than an Axe or large chopper
  It is much safer
  It consumes less energy to do the same job
  It helps keep your knife sharp by taking over much of the work
  It’s much quieter than chopping (you can sometimes hear someone chopping from a long distance away)
  It cuts much cleaner and therefore requires less finishing
  It is less destructive on green wood (more like pruning)
  You can saw through materials other than wood like PVC pipe, bone (hunting) etc.
  It’s cheap!
  Did I mention it’s safer? This is a very important and much under stressed point. I have heard of many serious axe accidents in the wilderness. An axe is not something you mess with and should not be used when tired, during low light situations, around young children, in tight spaces or by inexperienced operators. It can even cause serious injury by just lying around carelessly in a camp site.

My favorites are a compact saw, a sturdy 4” knife, a multi tool and a small axe. I might leave the axe at home or in the truck for shorter trips.