I did that on a Mac using the option key and a few custom key bindings.
The real question is how do you READ it. The problem is that unless you are very selective about your fonts and which characters you use, it can become impossible to read because many unicode characters are visually indistinguishable.
But that's not the actual point. Learning a new language is a challenge. Learning a new language when you haven't already learned 10 is an even bigger challenge. Learning your first language is very difficult, which most of us have probably forgotten. Now, to the list of things you have to learn to do so, we want to add learning several dozen brand new keystrokes that nobody knows offhand? It may not seem like much compared to everything else one has to learn to program, but having to learn a lot of stuff is annoying; having to fight your input devices is like being rendered mute. Try switching your keyboard map for a few days to see how you like it. This is not a level of frustration worth pursuing.
Capslock::F15I'm prepared to be corrected but ..
Greek capital sigma is the mathematical "sum" symbol just as capital pi is the product symbol.
The exceptions to this policy are usually writing systems that didn't have standardized encodings at the time they were incorporated into Unicode. Also, the rather notorious CJK unification project resulted in several new overlapping layouts as Unicode policy changed over time with respect to Chinese characters.
Added - they did; here is an older version (3.0) of the standard online http://www.unicode.org/book/u2.html