I definitely think that BECMI and other older basic edition including OSR clones, but also 5e, lend themselves pretty well to casual play. Then of course "casual DMing" is another matter! I wish I were able to improvise an adventure, but I can only improvise sandboxy encounters, not whole good stories and plots.
Outside D&D, I have been a player exactly in a casual heist adventure based on Risus, one of the rules-lightest RPGs I've ever seen. The DM was completely improvising the story, so it must be possible. In fact, the DM actually asked the players right at the beginning even what kind of adventure and in what kind of world we wanted to play, we made proposals and together voted for a heist adventure in a modern (slightly futuristic) non-magic setting. Storytelling was collaborative at times, and DM-based at others. It's hard for me to think of more "casual" than that