Wow, exciting idea. I've never heard that someone I know has such a co-writing experience. I can imagine writing a story together, but writing poetry or a speech on a different topic can be complicated because each person has their own opinion and feelings about this or that. Some time ago, I needed to write a speech with my friend, but I decided to do it myself after all. Here https://artscolumbia.org/free-essays/free-speech/
I found different examples, and in a few days, I managed to finish the speech. I mean, maybe writing with someone will save some time, but if I write something, I have my own vision of things and want to write the way I see things. Or maybe, I just haven't found the perfect writing partner.