I don't disagree that infix notation is more readable because humans have trouble balancing brackets visually. However, I maintain that readability doesn't seem to be the main concern of math notation. The main concern of math notation seems to be limiting ink or chalk use at the expense of nearly all else (especially readability). Why is exponentiation or log not infixed? Why so many different ways to represent division or differentiation?
It has persisted because it works, not because mathematicians are stuck in their ways.
Something persisting because it works does not imply any sort of optimality. A good way to test this is to find a paper with heavy use of esoteric math notation and translate that notation to code. I think you'll find the code more accessible. I think you'll find that even though it takes up significantly more characters, it reads much quicker than a dense array of symbols.
I spent a good few weeks trying to make sense of the rather short book "Universal Artificial Intelligence" by Marcus Hutter because he relies so heavily on symbolic notation. Now that I grasp it, I could explain it much more clearly in much less time to someone with much less background than I had going in to the book.