I've always viewed it kind of like minimized and obfuscated source code. If you took a program and replaced all of the variables with single (greek) letters and created custom notation for every type of function you would get something that looks a lot like mathematical notation.

People can certainly learn it, but it's hard to argue that it isn't a barrier to entry and has no doubt helped to turn many students off from mathematics.

I mean the primary reason a lot of our notation looks the way it does is so that it can be written compactly (paper was expensive) using quill pens. Is it so crazy to consider a world where mathematical language is more self documenting?