@Magi and
@Saintsman ... Let me try to better explain where I'm coming from here.
When you're skiing on edge, the point of force from the ski to the snow is pretty close to a single point, as you've described. However, the force from your boot to the ski is a distributed load (most closely represented by a triangular load). The largest force is on the edge of your boot that is closest to the snow. The force gently decreases as it gets to the edge of the ski that is raised up out of the snow (i.e. triangular distributed load). You can simplify this type of load by creating a single force vector. This vector is at the centroid of the triangular load (not the point of contact with the snow). Now if you have two people that are the same weight, one with wide feet, one with narrow. The same weight is distributed over a different amount of area (your boot), the difference in the location of the centroid of these two distributed loads is not much (if any difference).
@Saintsman and I are doing the same math you are - but are replacing the distributed load with an equivalent point load because the math and visualization are easier for the static moment. You aren't disagreeing with us or saying anything different.
If you take the example of two different width skis (one wide and one narrow) with the same boot and the same person, your distributed load is identical. However, your centroid of the distributed load is now closer to the edge of the narrow ski than the wide one. This makes it easier to put a narrow ski on edge, because your resultant force is closer to the edge.
An elegant way of repeating what Saintsman and I have already said, EXCEPT you're only examining what happens as the equivalent point load moves toward EQUAL with the foot.
I'm asking you to ALSO consider what happens when it flips to the other side. HINT: The DIRECTION of the default tipping moment reverses.
Thought experiment:
Imagine a table that has a top, a central shaft, and a circular stand at the bottom.
Imagine that the stand at the bottom is very small, and the top quite large relative to the bottom:
________________ Top
|
____ Bottom
Now imagine you push down on the edge of the table... Will the table tip over?*
Now imagine the the top is very small, and the bottom stand is relatively large:
____ Top
|
_________ Bottom
Now push down on the edge of the top of the table... will it tip over?**
The "Table" is a rigid example of the exact same system as the Tib&Fib/foot/boot/binding/ski, and the outcomes are the same. (Note that the way you can tip a ski that's wider than your foot [the table top] is that the rest of your upper body can move your CoM outside the edge of your ski.)***
So again - changing ratio of the width of the top of the system relative to the bottom changes the system such that three cases emerge:
Legs/foot have leverage (Ski narrower than edge of foot).
You are neutral (Ski same width as edge of foot).
Ski has leverage (Ski wider than edge of foot).
*Easily
**Literally impossible
***And to be clear - your upper body allows you to move your CoM outside of the system regardless of the situation because skis widths are <<< than the lateral distance you can move your CoM. (So I suppose that this *technically* only affects tipping with your lower legs, where you're actively never trying to shift your CoM from overtop of your ski's edge [and this is, again why wide skis tend to feel better to skiers that love to incline with the whole body]).