I thought running for a very long time without needing to surface was the entire point of nuclear subs?

It's not that simple. Launching an nuclear weapon from the deep is very hard, normal nuclear missile subs do not launch from deep. There are multiple reason for this. One of them is that they eject the missile by using steam/gas, if you are too deep, your missile won't reach the surface and thus won't be able to fly away. Second reason is that the missile and the missile tube needs to be under normal pressure. Missiles aren't built to handle hundreds of atmospheres of pressure even if the sub could eject them into the water.