Thank you for starting this discussion in the forum! I don’t have much experience with using TTRPGs in the classroom setting (I teach preschool kids), but I have thought a lot about GM-less variations of these kinds of games, and have enjoyed playing a few myself.
I have a small gaming group of friends who live in different parts of the world, and we get together now and then online to play RPGs. Due to the time differences and other responsibilities, it just doesn’t work for us to play something as involved and long-term as D&D, so I’ve been scouring the internet for simple one-shot games that are easy to put together and can be completed in a short time (our sessions are normally 2-3 hours). Many of these have involved a DM in a very minor role, mostly to get things started off, but one that was completely DM-less is The Quiet Year (https://buriedwithoutceremony.com/the-quiet-year).
In this game, players collaborate to create a world both narratively and through physical map-making. A deck of playing cards are used to determine certain questions and challenges that the players’ society must face, and the game has a built-in time limit as after moving from spring to winter (with the choices presented by the cards becoming increasingly morally difficult), an unavoidable disaster will end the story.
I think this would be a very interesting system to try in a classroom setting, with perhaps the teacher drawing the cards for the student groups as a whole, and then each group making their decisions and progressing with their individual group’s map/world/story. After the conclusion, groups might present to the class about their world and their choices.