these symbols CAN be redefined. the question is SHOULD they be redefined?

WHY? we should have a very good reason if we decide to do this. That very good reason had better be something amazing. There had better be some actual insight we didn't have before this redefinition that is impossible without it. But, if this redefinition were necessary, then it would also be complete. if we redefine these symbols, we should have a one to one mapping to their 'old' meaning. But, if we have that our amazing proof should also work with those old symbols.

TLDR; math is hard enough to discuss as it is. redefining everything for shits and giggles isn't helping anything.