I am not an historian nor an American, but my understanding is this:

The empowering Act of Congress was the Federal-Aid Highway Act of 1956, aka "National Interstate and Defense Highways Act of 1956". This Act specified the funding mechanisms to pay for Interstate Highways in the contiguous US (namely: Federal fuel and tyre taxes) as well as the type of roads funded (controlled access highways and regulated freeways. IE: no at-level intersections with crossing roads, use of on\off ramps, etc) and the purposes for those roads (primarily enabling of cross-country access in order to defend the United States during an attack or in times of war, but I'll assume interstate commerce was also a major factor).

The key part in Hawaii's case being the "Defence Highways" portion of the name: H-1 connects Hickam Air Force Base and Pearl Harbor with Honolulu. H-2 connects H-1 with Wheeler Army Airfield. H-3 was specifically built with Dept of Defence money to connect Marine Corps Base Hawaii with H-1. Hawaiians get these highways for the same reasons as Alaskans and Puerto Ricans: they are not exempt from the federal taxes, and have military assets worth connecting.

There's possibly other further enabling\funding legislation, but the highway policy of foreign countries is not my forté.