There won’t be a large amount of regular contributors to this forum who go mountain hiking with children.

We learned that our own is hugely stimulated by natural growth, so places with lots of biodiversity (trees, moss, fungi, flowers) energise her and she has the capacity to climb and walk for hours on end.
In more arid environments she did not have this stamina.
We could never do the long mountain hikes in Spain that we enjoyed in Japan when she was aged 6 to 11.
The upper parts of Fuji San are quite barren in comparison to smaller mountains. For us, this is the main reason I would not have considered taking our own child there.
Two days hiking in Yakushima, she would have thrived there as a ten year old.

As they say in Spain, each child is a world.
For our own, much as she likes great expansive views, they have never sustained her in the way the richness of a Japanese forest can.