As Acharis alluded to, I think you're confounding two different things: difficulty and play-style. Thing of them as axes that are orthogonal. One really has nothing to do with the other.

You're right that there are some problems created by providing different play styles instead of different difficulty levels, but I don't think they're completely unrelated, in that providing players with the option of a more comfortable play-style will make the game easier, whilst a less comfortable one will make it harder. You're absolutely right though that two players who prefer the same style of play might still enjoy a different level of challenge, and without a separate setting for difficulty you might also make things more difficult for players who have a poor understanding of their own strengths and weaknesses.


If you're treating different play-styles as entirely separate game modes you may also deny yourself the opportunity to provide variation in the game-play experience. Stealth games will sometimes allow the player to have a break by providing an "all guns blazing" scenario to mix things up a bit, and whilst the player could explicitly change change modes to try a different style that doesn't provide quite the same experience of having a break from the usual.