The integration of Federated Learning (FL) and Mixture-of-Experts (MoE) presents a compelling pathway for training more powerful, large-scale artificial intelligence models (LAMs) on decentralized data while preserving privacy. However, efficient federated training of these complex MoE-structured LAMs is hindered by significant system-level challenges, particularly in managing the interplay between heterogeneous client resources and the sophisticated coordination required for numerous specialized experts. This article highlights a critical, yet underexplored concept: the absence of robust quantitative strategies for dynamic client-expert alignment that holistically considers varying client capacities and the imperative for system-wise load balancing. Specifically, we propose a conceptual system design for intelligent client-expert alignment that incorporates dynamic fitness scoring, global expert load monitoring, and client capacity profiling. By tackling these systemic issues, we can unlock more scalable, efficient, and robust training mechanisms {with fewer communication rounds for convergence}, paving the way for the widespread deployment of large-scale federated MoE-structured LAMs in edge computing with ultra-high communication efficiency.