There's some context about river boards on Grand Canyon.
Almost 20 years ago, three women ran the entire Grand Canyon self supported on river boards. They even hauled film gear and made a movie about it (Three Women 300 miles). It's a good movie. Check it out.
Spoiler: when they first showed up for their launch, the ranger said that a board isn't a boat, and they were denied their launch. They worked a couple years and convinced the superintendent that the USCG considers them boats, so they should be allowed to go, and they were.
Since that time, the NPS has revised its rules so everybody knows up front that river boards aren't approved.
I wonder if there have been any incidents that prompted the NPS to list them specifically as not allowed. Paddle boards are allowed, but you probably won't be approved for self-support like you would in a kayak or canoe. I know people take packrafts, but they also wouldn't be approved as the sole crafts without any raft support. Same goes with surf boards; Laird paddled the whole thing on one, but it isn't an approved craft. The regs do discuss "secondary, discretionary use watercraft" (page
that includes paddle boards. I wonder if river boards are considered "secondary, discretionary use watercraft."