I think the 're-use as a sheiling' idea could explain why, if this is a prehistoric thing, it has been ignored.

Now I wouldn't know the remains of a chambered cairn from a random pile of rocks, but the upright stone does look a bit too big to be the kind of thing you'd expect to see in a sheiling, and the position at Elterwater is a prime spot due to it's commanding the approach to Langdale.

It would have been just the place to bung your prestiege monument if you wanted to make a statement about whose ancestors had dibs on the axe stone.