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: C-3 Eb3 G-3 Bb3
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.
As a US citizen who is a metric fan and loves using it, in what way? The government did switch - in the 70s - according to its own statutes, it had to.
It has crept up in various places (and I find it hilarious) innoculously, like in 2 liters of soda, or in how computer processors are talked about in mm² die areas.
But the average American still uses imperial units religiously, anywhere they approach a problem involving any unit of measurement they always default to imperial, and having a 14 year old brother I see no change in his education or habits to indicate a slow transition of mindshare. The government moved decades ago, but the people aren't moving at all.
I get the impression it is much like high school language classes - you learn it once early on, never practice it, and by the time you are a full adult you have completely forgotten it. I'm not sure how to improve the situation to actually get the people to start using international standards, because if you were to start trying to force it on the supply side people would just not buy metric tools and information because they forgot it back in primary school.
1. Make sure everyone is educated in metric
2. Change the easy things: the paper size the government uses, the units on food labels, the measures legal to use for sales of loose food or other goods, the units the government uses for all types of reporting. (Therefore if businesses want government contracts, they'll need to use metric.)
3. Change other standards, like residential construction, preferred fasteners, wire sizes. Where old measures are required for compatibility, write "24.5mm" in the standard. If the dimension could be changed to 25mm without any side effect, use that.
4. Change other things people see daily: I don't know if doctors use metric in the US, but I assume they communicate to patients in old units. Change the default, but accomodate older people. Change the road signs. Is anything left?
The UK is part way through 4, but has been stuck there for decades.
If there's a viable alternative to music notation that you know of and is superior to what we know as standard western notation, feel free to share.
Your choice of example is interesting, considering metric has won, and the US is switching slowly.
But there is no incorrect way of looking at it, music is an art. Standard notation is highly evolved and effective, it has been iterated on for millennia. Getting a critical mass of musicians to learn a newer system would be incredibly difficult. Both are true, and you can't compare them and say that one is "more", that's flatly not true in any meaningful sense.