I have spent some time with my nephew showing him basic wood working, and kids now, as Jimbo, noted are simply not using any kind of bladed tools in general and thus have a total lack of such skills and "common sense" about the tools. For felling, I would definately start them off with using a saw as part of the process, and for handling basic limbing and bucking. This makes the chopping much easier, which allows them to really go very light, and thus high on control. And also forces them to think step-by-step, instead of just walking away and starting to hack.
Regard to the edge, yes it will take a beating at first. But I think this is a good thing, as it will enforce the idea of proper swing technique, as long as you have them fix the edge which is just a necessary skill as being able to use the axe in the first place. You don't want to get them accepting of edge beatings, as then they won't place the necessary control on hit placement. The biggest thing is to get the force requirement down so they don't get frustrated. Around here we have a lot of clear pine which is great to learn on, as even with light chops you can get ~2" of penetration with a small hatchet.
In regards to hatchets vs light axe, I started on a small hatchet, so I am pretty biased towards that for the beginner, but I can definately see the advantage of getting the blade much further away from the user and of course keeping the head weight down. If you are going this way, the "Brush Axe" might be something to look at. It has no points, and is a good deal safer for the novice.
-Cliff