There's one more reason, which is that there are sometimes good reasons for writing your own sort routine. Specifically, if you have data that has a known distribution that lets you beat a comparison sort. One of the questions I was asked in a Google interview was along these lines. The point was not to see how well I could write code on a whiteboard or reproduce an algorithm from a textbook, it was to see if I could understand that the problem wasn't the same as 'sort arbitrary data', see if I could extract what properties of the problem made it amenable to optimisation, and see what tools I had for approaching that kind of optimisation.
And sometimes it's not about knowing if you can reproduce an algorithm, but about knowing whether you understand the limitations of a particular approach. Do you understand when that off-the-shelf quicksort library would do a terrible job on certain input data? In one interview, I discovered that my interviewer didn't know about hopscotch hash tables, but did know about cuckoo hashing, so we ended up with a discussion about what the overheads of the two approaches are and when either would be better.