In short, it is much easier for the agent to learn from a smaller dimensional state space. This is because the agent must also do representation learning; i.e. it must also infer what the state is telling it as part of the learning process. If you think of the architecture used in DQN to solve Atari, they had a CNN that outputted a vector which was then passed through some dense layers. Here the representation learning was done by the CNN and was trained using an end-to-end approach i.e. all updates to the network weights were done through the reinforcement learning objective; that is there is no supervised or unsupervised learning that takes place.
This can be particularly difficult when you combine images with sparse rewards as there is not a lot of feedback so the representation learning can take a long time. This paper gives a good description of the problem of decoupling representation learning from reinforcement learning with a nice solution.
The other main 'problem setting' I have seen images replaced with a latent state is when the authors are looking at planning. The problem with doing any kind of planning is that a model of the transition dynamics, $p(s' | s, a)$, is needed. For high dimensional state spaces such as images, this can be very difficult to predict and even relatively small errors will quickly compound so if you use the model to predict multiple time steps into the future the planner is useless because of these compounding errors. I think there is a discussion on this in this paper (certainly there will be references therein that point you in the right direction).