It's really tough to have a boot that's perfect for all environments. I've been in jungle environments where we needed water to drain quickly from our boots, we needed steel plates in the soles for booby trap protection. Durability was a concern.
In the mountains, we needed warm boots with soles suitable for slippery surfaces such as mud, ice and snow covered rocks (traction). Insulation was a must as well.
In the desert as you mentioned, keeping out sand or any other irritant would be a concern.
A boot that's not overly heavy is a must for all environments. I would also include a flexible boot that doesn't require "breaking in". Some comfortable inside sole cushion would be greatly appreciated as well. Whatever the boot is made from, it'd be good if it didn't need to be polished and shined (soldiers hate that).
These are just from my Infantryman's perspective. REMFs may have another viewpoint.