Recent years have seen a steady rise in the popularity and use of Conversational Agents (CA) for different applications, well before the more immediate impact of large language models. This rise has been accompanied by an extensive exploration and documentation of the challenges of designing and creating conversational agents. Focusing on a recent scoping review of the socio-technical challenges of CA creation, this opinion paper calls for an examination of the extent to which interdisciplinary collaboration (IDC) challenges might contribute towards socio-technical CA design challenges. The paper proposes a taxonomy of CA design challenges using IDC as a lens, and proposes practical strategies to overcome them which complement existing design principles. The paper invites future work to empirically verify suggested conceptual links and apply the proposed strategies within the space of CA design to evaluate their effectiveness.