I think your read is right on the money. There is an overall plot to the games, but the reason to play is in all of the ridiculous side quests, which are decidedly not serious: "Help this naked guy who forgot his clothes", "Help this guy make baby formula", "Stop the roomba gone rogue", etc

The games are a mashup of genres, but it is only the latest one which leans so heavily into the RPG aspects. Prior installments are more "fist fight dudes" core gameplay.