I think where this analogy fails is that it assumes the game player and the player character are the same and have the same goals. They're not. In your anime example, the game player would be some combination of the writer penning the script and the voice actor playing the role with the anime character being the player character.
The game player wants to win. They make decisions based on player knowledge to avoid, minimize, or circumvent obstacles, i.e. what they see as the win condition. The writer/actor also wants to win, however, their win condition is literally the opposite of the game player's, so the writer/actor does literally the opposite. They want to have good scenes to show off their writing/acting talents. Drama, earned growth, difficult obstacles, story beats, etc.
There's an obvious tension between these two sides. What makes for a good game (risk-reward, challenges, discovery, immersive fantasy, etc) and what makes for a good story (tension and release, rising stakes, etc) vs what most gamers seem to want (easy tensionless wins that make them and/or their character look good).
If the game player "wins" and scenes are "written" to their liking they would be the flattest, dullest scenes they can possibly be. "Gee, we won again with practically zero effort, no real risk, and no appreciable loss of resources. Huzzah." It would be literally the most boring anime you've ever watched. In fan fiction the term for this is Mary Sue or Marty Stu. Pure, bland as can be power fantasy. "I am the best, I am awesome. Praise me."
The writer/actor wants there to be drama and tension, obstacles and betrayals, all so they have something interesting to do. The game player wants none of that.