When it comes to doing a small independent play, or perhaps an improve show (obviously), o maybe some other student film, there are times when it can be appropriate to write your own monologue. Other than that, there’s not really any reason that someone would be able to do such a thing. When you write you own monologues, it doesn’t quite seem as professional as when you have one written from a legitimate play, or well-known author. It can actually also be seen as pretty unprofessional, like maybe you did not have enough time to find a “real” monologue, and do proper work on it, so you had to throw one together yourself.
As professionalism is one of the most important things to portray yourself with in the acting and entertainment industry, I would say to do your research, and make sure that you always have a professionally written monologue or two that you can use for a broad spectrum of auditions. It’s the best way to make yourself professional.