Why has there never existed an alternative musical notation system thats truely different?
Is horizontal lines and abstract squiggles with relative positions really the best we have?
For piano, there's Klavarskribo. If you've ever played Guitar Hero/Rockband, it's a bit like that: https://en.wikipedia.org/wiki/Klavarskribo
For many fretted stringed instruments, there's tablature. One line per string, and instead of abstract squiggles you get numbers that represent fret positions. They stack easily for chords, and there's intuitive notation for picking styles and such. E.g. sliding from the second to the fifth fret on the A string would look like:
E |----------
B |----------
G |----------
D |----------
A |---2/5----
E |----------
I see your point about a truly different system but, as music is basically sound through time, I'm not sure how else it could be notated if not linearly.
For Western classical, honestly, considering the information included in standard notation -- rhythmic complexity, phrasings, special symbols for various afflictions, etc. -- it would be really hard to replicate this in a system that's both easy for humans and computers to read. (Think if musicians had to use something like the piano roll found in most DAWs...)
There are plenty of alternatives, particularly when it comes to translating to a computer (see e.g. Lilypond notation). For many music projects that go from instrument straight into production without having to communicate to an intermediary performer, western music notation is unnecessary - piano rolls are sufficient. Piano rolls can also be useful in limited situations for performance (see Guitar Hero et al) but things fall apart quickly if you need to perform lots of different notes with sophisticated rhythms, and/or need to look significantly far ahead of the current point in time. (These are problems which Guitar Hero happily exploits as part of the game.)
The further away music gets from the Western classical music tradition, the more the notation system is stressed. Many of those traditions, however, are places where oral transmission of musical instructions are preferred, and where written notation may not be as developed. (See e.g. oral transmission systems for taiko and pakhawaj.)
Mass musical literacy is possible, as the American Sacred Harp tradition shows - but they didn't use regular notation.
Because musicians tend to be
1. conservative, so that they're unlikely to accept one,
2. elitist/guildlike, so that they don't especially mind barriers to entry, and
3. self-aggrandizing, so that of ten musicians inclined to propose an alternative notation, every one will suggest his own and ridicule the nine other proposals.
Western notation is really as bad as it seems, though - it encourages optical illusions (notes with opposed stems seem closer or further away from each other than they actually are, for instance) and is quite brittle (add a sixth line to a staff in the middle of the page, and many experienced sight readers will just play on and not notice anything is amiss except that the music suddenly got very strange).
Mass music literacy seems out of reach with the current notation systems. Even of people who can sight-read, many (probably most) do so by associating notes with instrument finger positions instead of intervals, so they can't read an unknown melody without their instrument at hand.
I think the most successful, more rational system is the number notation they use in China (which also has been reinvented many times in Europe). Funny that China should have the awkward writing system, but the sensible music notation system.
Most successful alternative notation systems seem to come from religious instructors, who were more concerned with helping the congregation to sing. Mass music literacy mattered from them in a way it didn't for professional musicians. Shape note is an American system (although an adaption of the regular one, still squiggles) and there are number notation systems in Scandinavia developed for the same reason, teaching the peasants to sing in four-part harmony. I wonder if the Chinese system doesn't have roots in missionary work, too - they use western numerals, after all.