Safety-critical software systems are those whose failure or malfunction could result in casualty and/or serious financial loss. In such systems, safety assurance cases (SACs) are an emerging approach that adopts a proactive strategy to produce structuralized safety justifications and arguments. While SACs are recommended in many software-intensive safety-critical domains, the lack of knowledge regarding the practitioners' perspectives on using SACs hinders effective adoption of this approach. To gain such knowledge, we interviewed nine practitioners and safety experts who focused on safety-critical software systems. In general, our participants found the SAC approach beneficial for communication of safety arguments and management of safety issues in a multidisciplinary setting. The challenges they faced when using SACs were primarily associated with (1) a lack of tool support, (2) insufficient process integration, and (3) scarcity of experienced personnel. To overcome those challenges, our participants suggested tactics that focused on creating direct safety arguments. Process and organizational adjustments are also needed to streamline SAC analysis and creation. Finally, our participants emphasized the importance of knowledge sharing about SACs across software-intensive safety-critical domains.