XML as a standard has a concept of "notations": you can specify that contents of an element are written in such-and-such notation, which can be "asciimath" too. Of course at the XML level these are merely labels; you still need to agree on notation names and make the processors of that document to understand that notation. But as a foundation it is there.

So technically a web could indeed be a different place: a network of XML documents where all the original notations are kept as they are and merely marked with tags that formally specify: this is AsciiMath, this is C, this is SQL, and so on.