If you're doing math, you need to be able to manipulate the symbols easily. These notations develop because they're easy to work with: consistency is less important than brevity. Lambda calculus terms may be easier to read, but they're much slower to write, and and they take up more space on the page or blackboard.

That said, once you've arrived at some kind of result, you could switch to a more consistent notation for explaining whatever you've found. It doesn't necessarily have to be textual, either (see http://worrydream.com/KillMath/).