This copies a post by grailly on Reddit.
Most games have adopted popular RPG mechanics and it's widely accepted that "everything's an RPG now". RPGs are also some of the biggest and most popular games around.
I'd argue that Puzzle Game mechanics (aka puzzles) are even more widespread than RPG mechanics throughout the media. However, Puzzle Games themselves are pretty niche and basically never get any big budget titles. This gets more surprising when realizing Puzzle Games are very popular; Tetris might just be the most recognizable video game, Portal (Portal 2 might be the only AAA puzzle game?!) is insanely beloved, wordle took the world by storm last year, sudoku and crosswords are still in the newspaper every day, Candy Crush...
Why do you think Puzzle Games are relegated to being indie or AA?
I thought about it a bit and came up with some unbaked responses which I hope you will add to:
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People want to kill stuff in AAA games. To which I answer, can't we kill stuff in puzzle games?
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There's little point to making Puzzle Games more expensive. Would having The Witness or Talos Principle pushed to AAA status make them any better?
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"Puzzle" is a recessive genre. Add anything to a puzzle game and they aren't considered puzzle games anymore. So making a AAA Puzzle game will basically remove its Puzzle Game consideration. Puzzle + exploration = adventure. Puzzle + fighting = Action adventure. Puzzle + story = walking simulator, etc.
What is BOTW if not an amplified puzzle game? The core mechanic aside from the open world is literally to enter small isolated puzzles and to solve them. Zelda in general is heavily reliant on puzzles, are they not puzzle games? What about detective games and point and click games like Myst, Monkey Island, what are they?
There are many mobile games like Candy Crush or Angry bird.
So essentially something like Thief or Dishonored where you need to find a path in a level?
I believe you're being very reductive by saying we don't have AAA puzzle games. Yes we don't have AAA tetris-like because they don't need ultra HD graphics or first person viewpoint and therefore they have some limits, but puzzles have definitely been incorporated in many games.