There is no rational reason. The US can put as many military resources as it likes there, and the fact that they haven't probably points to it not being a great place to station a larger force because of the climate. US companies can mine there if they're able - it's not currently economic to do so due to the climate and glacier.
You can't just go mine there. For one no-one can own land. A permit is also not something you just get and the laws protecting the environment are much harsher than US laws.
So I guess we have to look to irrational reasons.