"Recommender Systems" is a very broad area and can be approached from different optics: latent variable models, graph models, etc.
"Deep learning" is an umbrella term for gradient-based optimization of deep differentiable models, and has been used to model all sorts of supervised learning problems, including graphs and latent variable models. Therefore, it has been applied to many different areas, with a great degree of success.
Multiple deep learning approaches have been applied to recommender systems because deep learning performed well in many other areas, so why not expect it to perform well for recommender systems.
Neural approaches have proven to be effective also for recommender systems. That is why they are used nowadays.
Also, different inductive biases have been applied to neural networks in other areas and, in some cases, such inductive biases are also useful for recommendation, like the sequential bias for recurrent networks, or the structured bias for graph neural networks.
If you want to explore the academic publications related to neural recommender systems, I would suggest that you start with the article Neural collaborative filtering and the survey Deep learning based recommender system: A survey and new perspectives.
Also, in order to get a broad view of the state of the art in recommender systems, you may have a look at papers with code, where you can see the best-performing systems for different benchmark datasets, with links to the associated articles and source code repositories.