Although high places can be strategically important to hold, when on the march they may yet offer a net disadvantage.
High places are not the same as smaller hills which give sight all around and which can be comfortably defended.
High places can be bare, cold and lack resources for keeping the army fed. Armies in high places may also be spotted from multiple other locations.
High places can leave you with your back to a mountain with the only route being down. This can lead to you becoming trapped.
Valleys offer more space in which to manoeuver. You can hide a large army in a valley, with only a few sentries in the high places to prevent ambush.