Maybe sheet music can be improved upon, but the real question is should it? Sheet music is easy enough to learn, and once you learn it, all music opens up to you.
And, all that being said, learning to read music is really not very difficult. There seem to be a lot of complaints from the HN crowd about music notation, but learning to read music is wayyy easier than learning a new programming language. Seriously, just get over it and learn the system that everybody else uses, and you will be able to play any piece in just about any repertoire on the planet.
Granted, sight-reading skill is a matter of degree. I can read a jazz band gig, but would struggle with complex modern orchestral music. In musical styles that I'm familiar with, I can often make a good enough guess about what's next, that I only have to focus my attention on the dangerous bits. My attention often wanders away from the page.
I used to think that sight-reading was something that had to be learned, starting at an early age. I don't know if I still believe that, but I know that most adults who attempt to learn, find it to be prohibitive. This is one reason why it would be great to find an alternative. Even a piano with keys that light up.
Of course, it is not exactly a substitute for sheet music, but it is eminently readable to the novice.
However, you can't create such a notation for every situation because, some times, piano pieces are hard and notation is not going to make things easier. There's hardly a way to clearly see the notes you have to play and their timing when there're multiple notes in different melodic lines. with different rythms: it's just hard and it's not because of the notation.
I wouldn't say it's not challenging, but it's out of place, thus tedious. As other people said, it's an abstraction for people doing the art, IMVHO it's not important unless you are doing the art.
But it's not just for pedagogy. It's a practical tool for musicians, because it lets you throw people together to make coherent music quickly. This could be just playing string quartets in somebody's living room, or running a large performing ensemble. The size of one band that I'm in virtually ensures that there will be at least one new member or substitute at every performance. The ability of players who can read the stuff influences what can be composed.
And a lot of this music isn't even commercially viable for the people who play it (such as in my case), but there's just the enjoyment of exploring the world of written music.