I remember in the good ol' days, there would be forums that would have a dedicated section for RP. It was one of my favorite sections and really sparked my interest in creative writing and role play to the point where I even branched out and played on sites that were fully dedicated to RP. We would play multiple characters and spend hours talking about our characters and actually participating in the RP. In hindsight, it was probably a deterrent from anyone else who may have wanted to participate, but I remember having loads of fun and now use that mentality to shape how I do RP nowadays when I actually participate in them by creating characters that have specific plots with specific characters while also keeping my options open for other players who may want to get involved to foster a fun, welcoming environment. (I should remember those words the next time I find the drive to try and find an RP site to participate on lol.)
I feel like games like D&D are best played in real time though. I play irl with friends and we have a specific day and time that we meet each week (or in the case of my Wednesday game, twice a month) to play and continue the story, but it's open enough that new players can be added into the story whenever or if someone has to miss a week (or several), they can still be brought back in while also letting their actions from the session(s) they were there still take part in the overall campaign. In my Wednesday game, we just wrapped up a campaign where we had a player take parts from a vehicle to use on their own character, and said vehicle was brought into the game by another player who only came for one session. My other game, I haven't participated in the actual story yet, but I was able to participate in a side event that the DM started the first week I came and still get the opportunity to interact with the other players and start getting to know everyone. That game, there's also a Discord server for us all to talk in between sessions, and my other game is working on getting something set up too.
But I've also participated in games set up online with online friends, but still played in real time. Those games also went well, but they ended up fizzling out because of availability issues, which then led to us all just no longer doing the sessions as a whole. I still enjoyed the brief time we played together, but the games fizzling out quickly were a bummer.
I think if something like this were to be run on a forum, it would definitely need to be kept engaging and the story pushed along to keep players interested. A brief sign up period would be ideal to get the initial batch of players, but maybe also keeping it open to allow others the option to join in if they wished. Probably running it similar to how forum Mafia games are run, where there's a set time frame in which players have to post their characters' actions before the DM comes in to move things along. Gives people time to read and post without feeling too rushed, but if they can't make a post within that time frame, then there's no major repercussions. Combat and dice rolls would probably be the tricky part, and honestly, what makes me believe that a game like D&D would be best played in real time with organization and general discussion happening on the forum and the actual action happening on Discord (or another alternative, like Roll20). Other game nights I feel the same way about: organize on the forum, then the actual event happens on Discord so people can talk and interact as they play.