What are the pros and cons of using a supervised learning approach for building a recommender system compared to traditional approaches? Pretty much all articles I read about recommender systems use Collaborative Filtering, Content Based Filtering and Hybrid approaches. Virtually no one mentioned about supervised learning approaches. We can use ratings/clicks as the target variable and user attributes and item attributes as features to build a classification/regression model and use the predictions from the model to do recommendations. Are there any particular reasons for such an approach being ignored in the recommender system community?

As @Tim mentions, supervised learning is widely used in recommender systems. Common recommender systems like Collaborative Filtering, Matrix Factorization, and Neural network based methods rely on the availability of labels provided by the previous interactions between users and items.

We can use ratings/clicks as the target variable and user attributes
and item attributes as features to build a classification/regression
model... Are there any particular reasons for such an approach being
ignored in the recommender system community?

Based on the above part of your question, I assume you're asking about the use of some specific types of supervised learning, i.e., models similar to linear and logistic regression. Below, I provide examples of these types of models (or those that are inspired from such models) that have been proposed for recommender systems. These are well known models.

*

*SLIM: Sparse Linear Methods for Top-N Recommender Systems

*Logistic Matrix Factorization (pdf)

*Two-Class Collaborative Filtering (pdf)
