I agree that they can make "auto-themed" flat rides that are technically still "immersive," e.g., Dino-Rama at Disney's Animal Kingdom being themed as a carnival, but IMHO that usually comes across as a transparent retroactive rationalization to install inexpensive amusement park rides in a themed environment (or, worse, the backstory isn't obvious to guests, who thus interpret it simply as a non-immersive amusement park within a theme park, e.g., Dino-Rama again).
That said, something like what you suggested - a carousel in a park-themed subsection - would probably be among the least-intrusive / most-successfully-fitting options.