The cost to bore tunnels would be extreme, and likely would deter investors.
I don't have an obvious solution for that, but no one said park preservation and tackling global warming would come cheap.
On top of that, where do you put the waste rock, which can be metal leaching or acid generating.
I don't know much about this, but as the tunnel is built, use it to truck out the waste rock, which can then be shipped outside of Alaska to be processed and handled in the usual processing plants in the US (or even pay to handle it overseas). Again, costs, but same answer as above.
Hmm. Could the rivers be made navigable without hurting the surrounding ecosystem too much? Or maybe an artificial canal .. but I suppose a new canal has many of the same problems that a new road (or roads) would entail..