Classic music notation is pretty and all, but it's about 1000x easier to learn (and read, even if you know how to read music) this: http://www.youtube.com/watch?v=7O93rQtWJVM
Agreed. That (youtube) method may be better for non-musical people who haven't actually learned but... if they spent the time learning to read music they'd find it far better.
Classical music isn't just pretty. It's the written language a composer uses to communicate musical ideas to a performer. It's highly expressive. Many trained musicians can sight-read a piece of music on the fly and make it sound wonderful.
What you linked a cool idea for helping people visualize notes on a piano but is nothing close to a replacement for real written music.
Here are a few reasons why traditional musical notation is far superior to timed falling bars (such as this Synthesia thing, or Guitar Hero, Rock Band, etc). These are elements which provide important and useful information and detail to the performer.
... and on and on. Traditional notation has worked really well for hundreds of years. Once learned, it is not so mystical or difficult, and actually makes a lot of sense.