Hardware heterogeneity across diverse user devices poses new challenges for beam-based communication in 5G and beyond. This heterogeneity limits the applicability of machine learning (ML)-based algorithms. This article highlights the critical need to treat hardware heterogeneity as a first-class design concern in ML-aided beam management. We analyze key failure modes in the presence of heterogeneity and present case studies demonstrating their performance impact. Finally, we discuss potential strategies to improve generalization in beam management.