I certainly agree that communication can be improved (and this is one of the main reasons I spend so much of my time improving my technical communication skills

I certainly agree that communication can be improved (and this is one of the main reasons I spend so much of my time improving my technical communication skills via blogging). But I stand by my defense of the need for flexibility. It's extremely hard to explain why without delving into technical details, but there are some times when abuses of notation are honestly much more helpful than they are hurtful. Usually they exist to decrease the amount of clutter in syntax, and they are often stated in words during presentation (and the abuses mostly go assumed only in the higher-end research papers, in fields where the fundamental book every practitioner is obligated to read spells out all of those assumptions in full). Of course, the more of these you add on the harder it becomes to explain it to a newcomer. So I'm not trying to defend the math culture as being right in all ways. I'm just trying to explain why things are the way they are, and rationally see that there is a good reason to do so (or else why would it have been done?). When you learn the stuff in real life, each of these "abuses" are added on one small step at a time (maybe I learn about one new abuse of syntax every month or two) and so absorbing it all simultaneously is not such a big deal.