First off, if you haven’t seen it yet: CarPG is a new diceless rules-lite RPG framework written by my buddy Matt Bryant (the guy behind Main Sequence.)
While he designed it as a game to play on road trips with your buds, I’ve found it incredibly useful as a mechanic for playing Play By Post rpgs. In my past experience, play-by-posts worked either one of three ways: 1) The dice rolls were either handled completely by the moderator, leaving a sense of control out for the players. 2) The entire game was purely narrative focused, which while fun often felt more like a writing exercise than a game. And then lastly, 3) The die rolls were handled like normal (either on the honor system or with online dice rollers), and as a result the game system itself really bogged down the pace of the game.