With the advent of technology we may see different ways of communicating music to each other crop up that rival standard notation, but its just not standardized yet.
Notation does leave out some variables, but not many. Dynamics, feel, style, can all be notated. Sure, note length is pretty much "set", but you can suggest a style to play in and the player will know what to do. But you are correct in that it comes down to individual interpretation and that one player may play it differently than the other.
All this is moot though unless you have a better way of doing things. Standard notation is still the standard and for good reason.
Sure - although I have some ideas (something like a 2-d version of the Nashville number system, but numbered 0-11...) But I'm sure no-one else would like that!
Still, the OP was basically asking if SN was worth learning, which is not the same question as 'Is SN as good as we can do?'
I'm not even sure why we would need the accuracy you are suggesting with regards to note lengths.
Let's say you didn't have a computer or a recorder - and you wanted to preserve for eternity a really funky rhythm that made a lot of use of subtle swing and little timing pushes and pulls...
But as I said, timing isn't the worst thing about standard notation - it's the 'C Major is king' nonsense!