As cloud infrastructure becomes the backbone of modern organizations, the security of cryptographic key management, especially using Hardware Security Modules (HSMs) and Trusted Platform Modules (TPMs), faces unprecedented challenges. While these hardware-based solutions offer strong protection in isolated environments, their effectiveness is being undermined by cloud-native threats such as misconfigurations, compromised APIs, and lateral privilege escalations. This paper presents a comprehensive analysis of publicly disclosed attacks and breaches involving HSMs and TPMs in cloud environments, identifying recurring architectural and operational flaws. We propose a taxonomy of attack vectors based on real-world case studies and threat intelligence reports, highlighting the gaps between hardware trust anchors and dynamic cloud ecosystems. Furthermore, we evaluate emerging defensive paradigms: confidential computing, post-quantum cryptography, and decentralized key management systems (dKMS), assessing their potential to address these gaps. Our findings emphasize that securing cloud-based cryptographic trust requires a layered, context-aware approach that integrates both hardware and software safeguards. The study serves as a practical framework for cloud architects and security engineers to reassess key protection strategies in light of evolving threats. To our knowledge, this is the first work to synthesize documented, real-world cloud HSM and TPM failures into a coherent taxonomy grounded in modern threat models.