At its core, musical notation is succinct: a mixture of logic and unique symbols. Note markers are isomorphic to pitch. Rhythms subdivide with vertical lines. Special symbols and brief phrases denote beginnings, ends and loop points. (They're not usually in English) Geometric figures indicate volume and speed changes.
A competing system in my purview is "tracker" notation. It's vertical and generally only used on machines, but hand writable: It looks like:
I think a valid comparison is the regular alphabet. It is, after all, a coding system for language in the same way that notation is a coding system for music. Most of the problems of that coding system (my pet peeve is english spelling) generally stem from conventions rather than problems with the alphabet (italian and german is much easier to spell correctly).
There might be some interesting alternatives (hangul!), but those systems come with their own share of problems and generally have no big benefits. I actually believe that musical notation is better fit for it's task than our current coding system for language.