A few major challenges:
- Designing a game that is fun and intuitive to play with a wide variety of input controllers (touch, mouse, keyboard, joystick).
- Handling the entire spectrum of screen resolutions, from older iPhones to high-end desktop computers. The game would also probably need to work in both portrait and landscape modes.
- The QA effort alone could be huge. Testing on quirky desktop browsers or buggy Android devices alone could be a dealbreaker.
- I'd argue that the time spent trying to figure out a game design or technical workaround for a particular platform would be better spent focusing on one platform and making the game more fun. In my experience, trying to make a fun game involves a lot of trial and error and iteration, and I personally don't think I could do it if I also had to keep in mind multiple distinct target platforms.
I can envision a couple one-button games like Angry Birds or Tiny Wings possibly having a chance, but even in those cases, I'd argue it'd be better to nail one platform first and then incrementally add other platforms instead of spreading oneself too thin.