Why would either of them die when they are some of the greatest tools ever invented and there is nothing better for the typical use case?
I have absolutely no idea why pivot tables would die before spreadsheet software. If people are using spreadsheet software, of course pivot tables will be useful. So to put my stack overflow hat on, it's asking the wrong question. Its entirely a matter of whether or not spreadsheet software has a place.
It's the best tool I never want to work with.