Moreover, there are games that are best described as "Action-Adventure." The Zelda series effectively started it, I think. It denotes a game in which there is action, but in which the action is not necessarily the main focus, or at least not the sole focus. Like a traditional adventure game (Zork, King's Quest), there is an emphasis on exploration, inventory management, experimentation, puzzle-solving, and some kind of a "quest" narrative. An Action-Adventure game is goal driven rather than score driven--which was not yet an assumption as it is with most single-player games today. It has elements of an action game and elements of an adventure game: hence "Action-Adventure."
Looking back to the advent of the first Zelda game, no other genre could have better described the game. It lacked the vestiges of pen-and-paper games that define the "RPG" genre of video games. "Action" was considered a genre at the time, but would have been at odds with the adventure element of the game. "Adventure" was an established genre, but would have been at odds with the action element of the game. "Hack and Slash" was not a named genre at the time, as far as I am aware. Had it been, it would have described Gauntlet and little else. The name "Hack and Slash" describes games where the player must (often mindlessly) repetitively cut a swath through near-endless waves of enemies almost constantly. This does not describe any of the Zelda games, even if the genre existed at the time the first one was made. "Action-Adventure" is the best choice.
There are clearly other games that have followed the example of the Zelda games, so the genre is neither empty, or should it be a catch-all even though some may use it that way.
Just more food for thought, but Diablo belongs to a much older established genre of "Roguelike" games. Because Diablo and Diablo II are Roguelikes, and these are the primary example of a "hack and slash" does this render the "hack and slash" genre nonexistent?