Alright, I agree with you that how adaptable difficulty is implemented is really the key to its success or failure, but I'm still not 100% convinced that a game will always be able to interpret what difficulty the player wants just based on their style of play. If you're running and gunning in Bioshock, you're playing in a distinctly different way that the game can detect and adjust to.

But what if two players are playing the same way, with the same skill level, but have a different threshold of how many times they die without getting frustrated? The game can't necessarily detect that from in-game data.

For the record, I'm not at all opposed to adaptive difficulty, as long as there are other ways to adjust the gameplay experience (like predetermined difficulty levels)

As long as a game has pre-defined difficulty levels, you can pick what level of difficulty you want, both in terms of what you're capable of, and what you enjoy. If its adaptive, then then game decides what level of difficulty you should be playing, based on your skill. My point was that a player's preferance of difficulty may not be based solely on skill.

But games are about entertainment, not necessarily teaching a skill. Its not only about what skill level a player is capable of, its about what level of challenge they find enjoyable. Two gamers of the same skill level may want different experiences. One may love a difficult challenge that pushes their skills to the limit, where one may want a more casual experience. When a game scales just to the player's skill level, the player loses the ability to chose what kind of experience they enjoy the most.