You are missing the point. I could proclaim that from now on we are going to use the /$ character sequence to implement the integration function in a hypothetical language. I could similarly continue with that idea and create a bunch of transliterations and cover a wide range of functionality. And, yes, people would be able to learn it and learn to read it. One example of this is reading regular expressions.
However, having that that, you have not created a new tool for thought all you have created is the ability to --as I described it before because I despise it-- vomit a bunch of ASCII characters into a file and call it a program.
Notation is powerful. The association of symbols or icons with ideas is powerful. The play, stop, fast forward, fast rewind and other buttons on your remote are easy to recognize, read and use. You could purposely avoid using symbols and use words: "FFWD", "STOP", "PLAY", etc. However, using symbols (notation) is by far the most efficient and communicable tool.
Going back to the integral, well, the existing mathematical integral symbol conveys the entire concept very efficiently.
J, to some extent, comes from an era when it was downright painful to even attempt to print or display APL characters. You had to replace character ROMs in printers, graphics cards and terminals. You had to replace print heads on other machines. APL characters before expanded character sets and the ubiquity of GUI-based operating systems were painful to implement and communicate. J attempted to solve this by transliterating from the APL symbol set to an ASCII-based equivalent. When that happened one of the most powerful aspects of APL was thrown out the window.
That's why I call J an abomination. The functionality offered by J is probably an improvement of APL. However, walking away from attaching meaning to custom symbols was a huge step backwards. Perhaps Iverson thought the reason APL was not seeing wider adoption was the character set, gave in and sought to fix it by going to ASCII. In my not-so-humble opinion, that was a huge mistake. ASCII is gibberish. Symbols, much like a page full of mathematical equations, means creating and using a new language that become part of your mental process.