Ask a simple question, get a simple answer: no. While there are some programmers who develop libraries, the majority will just consume well-understood sorting algorithms which are baked into their languages/standard libraries/etc of choice. If you find yourself coding mergesort and you are not in a job interview, a nightmare, or a nightmare of a job interview, you are probably doing something wrong.
That said, most of the reason we teach sorting algorithms is to teach algorithms in general, and particularly the consequential lesson that "There are often many methods to doing something that work; these methods are often different in extraordinarily consequential ways; the right method for certain problems -- even ones which look trivial on the outside! --may require literally years of R&D to develop."
That said, most of the reason we teach sorting algorithms is to teach algorithms in general, and particularly the consequential lesson that "There are often many methods to doing something that work; these methods are often different in extraordinarily consequential ways; the right method for certain problems -- even ones which look trivial on the outside! --may require literally years of R&D to develop."