But... wouldn't it be better to burn a fire at high elevations, presuming you've brought in your own wood or fuel? Trees become very sparse at these elevations and temperatures are relatively low.
The sparseness of trees is exactly the reason not to allow fires. In your example, Okanogan-Wenatchee NF is pretty far north (east of Seattle), so the tree line is probably pretty low in elevation. If you saw that trees were sparse, then it was because you were approaching the tree line. The tree line is by definition the boundary of the forest ecosystem, where trees can just barely survive. A tree at this elevation can be 300 years old but only 10 feet tall -- this is called krummholtzing, and it occurs because the growth rate is so low.
If camp fires are allowed, then people will scavenge the landscape near their campsite for wood. In an ecosystem where trees have this much difficulty surviving, we don't want that. People will of course always claim that the wood they used was already dead. Actually, the dead wood is important organic debris that forms part of the basis for building soil from dead rock.
But why not allow burning, say, wood pellets or briquettes which would obviously be brought in from outside the park?
These regulations are written with high-elevation backcountry areas in mind, not car-camping campsites. Backpackers aren't going to carry briquettes with them.
And even at a car-camping campsite, it's not a good thing if people bring wood from other areas to burn. This brings in harmful insects and other disease causing organisms that the trees in the area don't have natural resistance to, and it's why you'll see signs saying "Burn it where you buy it."
The original question seems predicated on the assumption that it's really important to have a campfire. It's not. Building campfires all the time is a habit from the middle of the 20th century. It's environmentally destructive. Just don't do it. You can enjoy yourself in lots of ways without a campfire.