In recent years, a growing number of deep model-based reinforcement learning (RL) methods have been introduced. The interest in deep model-based RL is not surprising, given its many potential benefits, such as higher sample efficiency and the potential for fast adaption to changes in the environment. However, we demonstrate, using an improved version of the recently introduced Local Change Adaptation (LoCA) setup, that the well-known model-based methods PlaNet and DreamerV2 adapt poorly to local environmental changes. Combined with prior work that made a similar observation about the other popular model-based method, MuZero, a trend emerges that suggests that current deep model-based methods have serious limitations. We dive deeper into the causes of this poor adaptivity, by identifying elements that hurt adaptive behavior and linking these to underlying techniques frequently used in deep model-based RL. We empirically validate these insights in the case of linear function approximation by demonstrating that a modified version of linear Dyna achieves effective adaptation to local changes.