Terry, I can speak from a machine shop perspective. Helicoils are great when it makes sense to have a machine thread on the inside and outside of the insert, say when inserting into metals. They are most frequently used to put a durable screw hole in a softer metal, say aluminum, or to repair stripped threads in a variety of metals. They make a lot of sense when space is tight, as the helicoil hole size is not too much larger than the screw size. The typical procedure is to drill and tap a larger hole, thread the helicoil in with a special tool (which threads into the helicoil and hooks the tang at the bottom -- this action "winds" the helicoil to a slightly smaller diameter while going in), then break off the tang (such that you get a through hole). You can place small stakes at the opening of the helicoil to prevent it from backing out, or some people use Devcon or Loctite to glue them in, though that's rare. The same tang effect that makes the helicoil wind smaller when driving in means that it springs back to a larger diameter when the driving tool is removed, thus helping to keep it snug in the hole. I hope that makes sense; when unused, helicoils relax to a large diameter; when driven in by the tang, they wind to a smaller diameter; when released in the hole, they settle in to an intermediate diameter that is snug in the hole.
While I have used helicoils in soft materials (even pine), the act of breaking off the tang can loosen up the repair. And, it's not usually appropriate to put machine-threads in soft materials, such as what is needed to thread a helicoil in. This is where inserts make more sense. You can get inserts with more aggressive wood threads on the outside, and they also can be driven in with a screwdriver from the top -- most inserts have slots at the top. Thus, no need to break off a tang. Inserts can be epoxied in as needed.
I think skis are somewhat of a gray area, since the #12AB thread is already very close to a machine thread and ski topsheets are fairly hard. I think helicoils and inserts can work fine here, but ultimately it would depend on the topsheet material. Certainly, helicoils might be preferred if they result in a more compact repair.
There are also those repair doo-dad anchors that you press into a hole, and they simply add material between the screw and the hole. This is a more fancy way of packing a hole, like some people do with steel or lead wool (or even toothpicks).