Hi geoff - seems like you are pretty knowledgeable here. I have to disagree with "seems forecasting actual rain is not very hard if you have enough current data on the state of the atmosphere" ... Who told you that? accuweather meteologists?
Rain is not easy predict, especially long in advance. Just taking things with a grain of salt here. If you truly believe that forecasting actual rain is not very hard, please start a new weather forecasting company and give it all you got! However i'll tell you, it's not that easy. Just because a computer model 'runs' does not mean it correctly modeled the atmosphere. All models are imperfect bud and those imperfections get amplified by 10x when trying to simulate earth+atmosphere systems