In my opinion, there is something about your approach in showing the flying through a big city with an helicopter, in terms of graphics/audio/ physics, that evokes a particular sense of freedom (especially at night). The idea of a copter-driver job (but not necessarily only as taxy driver) it's new and could be explored through many game modes: a would prefer a free-carreer-mode/build-your-own-company experience (without a fixed or semi-scripted storyline). In these game types, usually are audio/physics and logics that really keeps the gamer attention hight. However a more study in deep of procedural detail generation, random events (for instance in passengers/clients interaction) and a movie-like graphics enhancements (in terms of lights, colors, textures and environment dynamics in sky and ground) could take this game to a new level of entertainment, where it's like you're discovering something new every time you play.
For what concerns time trials challenges, maybe they can be integrated in the taxy job itself: for instance, some passenger may need a fast run towards his destination, but for some reason you can't flight where you want (and so you're forced to fly even between buildings as fast as possible).
I hope you'll find the right alchemy in mixing all these elements (and/or finding new better ones)!.
Thanks for your attentions.