Fluid-structure interaction (FSI) dynamics within pipeline systems continues to be a pivotal domain in FSI research. The FSI transfer matrix method for multibody systems (FSIMSTMM) demonstrates high computational efficiency owing to its low-dimensional global transfer matrices, thereby rendering it widely applicable in FSI dynamics simulations. Nevertheless, this approach encounters numerical stability issues when handling high-frequency calculations. While existing studies have proposed the reduced FSIMSTMM to enhance computational stability, the underlying mechanisms by which this reduction improves stability remain insufficiently explored. To address this gap, the present study employs an FSI multibody system transfer matrix model to systematically clarify the role of the reduced FSIMSTMM in enhancing numerical stability throughout the entire computational workflow. The findings provide theoretical and practical insights for optimizing high-frequency FSI pipeline dynamics analyses.