I'm afraid you are overstating the importance of alphabets. For example, try this: http://nedhardy.com/2012/04/25/learn-korean-in-15-minutes-ye... It's not really hard to learn alphabets.

I feel the traditional notation achieves a good tradeoff between clarity and conciseness. I don't want to write the string "integral(sin(x),0,1,x)" on paper - 22 symbols - traditional notation is much more concise. I hate to write parens in (a+b)/c; traditional fractions are clearer. On the other extreme, think about programming in APL.

Also see http://terrytao.wordpress.com/career-advice/there%E2%80%99s-...