Weakly supervised learning is a popular approach for training machine learning models in low-resource settings. Instead of requesting high-quality yet costly human annotations, it allows training models with noisy annotations obtained from various weak sources. Recently, many sophisticated approaches have been proposed for robust training under label noise, reporting impressive results. In this paper, we revisit the setup of these approaches and find that the benefits brought by these approaches are significantly overestimated. Specifically, we find that the success of existing weakly supervised learning approaches heavily relies on the availability of clean validation samples which, as we show, can be leveraged much more efficiently by simply training on them. After using these clean labels in training, the advantages of using these sophisticated approaches are mostly wiped out. This remains true even when reducing the size of the available clean data to just five samples per class, making these approaches impractical. To understand the true value of weakly supervised learning, we thoroughly analyze diverse NLP datasets and tasks to ascertain when and why weakly supervised approaches work. Based on our findings, we provide recommendations for future research.