There's a certain irony in the idea that Hawaii has interstates, given that it's an archipelago. It's great that H1, H2, and H3 exist, and Hawaii deserves the same road funding as any other state. But there's some lesson about naming conventions, or emergent properties, or maybe something else to be had here for sure.
The interstate highway system is actually made up of Interstate and Defense Highways. So all the "interstates" in Hawaii are actually Defense Highways that connect Pearl Harbor with other military bases on Oahu.
- The H-1 goes from Barbers Point to Pearl Harbor to Diamond Head.
- The H-2 connects Pearl Harbor with Schofield Barracks.
- The H-3 connects Pearl Harbor with MCBH (Marine Corps Base Hawaii) at Kaneohe.
I presume in Alaska's case, at least, it's a funding technicality. As you said, the roads are not built to interstate standards (with a few exceptions around Fairbanks and Anchorage, maybe). For example, without prior knowledge, no one is going to guess that the AlCan is an interstate, as there aren't even any signs indicating such.
