Why climate models are so expensive to compute?

Climate models are usually very expensive to run. On supercomputers, it often takes months to get results. Are those results of high quality?  No! The very opposite is true. For years, climate models predict widespread desertification on Earth. But Earth gets greener in the last several decades. This is very easy to understand. CO2 is the food for plants. More CO2, more food for plants, Earth gets greener. It is that simple!

If so, why climate models are so expensive to compute? When the computation gets so expensive, only well funded people get to do the computation. Since funding is controlled by the powerful, only those who follow the order from the powerful get funding to do the computation. By making computation, and research in general, very expensive, it excludes anyone who seek truth instead of approval from doing research.