Path-aware networking (PAN) architectures, such as SCION and emerging LEO constellations, expose tens to hundreds of verifiable paths to endpoints. When multipath protocols like MPTCP and MPQUIC greedily exploit this diversity, uncoordinated migration can induce persistent, high-amplitude load oscillations. Although this instability is well-known, its quantitative performance impact remains poorly understood. In this paper, we apply a discrete-time axiomatic framework to the joint dynamics of loss-based congestion control and greedy path selection. By deriving the system's dynamic equilibria (stable periodic oscillations), we prove a fundamental trade-off: high Responsiveness improves Fairness but necessarily degrades Efficiency and Convergence. Conversely, we demonstrate that Efficiency, Convergence, and Loss Avoidance are simultaneously achievable at a critical lossless operating point. Furthermore, we find that while migration de-synchronizes traffic in high-diversity environments, realistic limited-visibility constraints transform coherent oscillations into persistent spatial load imbalance, rather than eliminating instability entirely. These results yield concrete design guidelines for robust multipath transport over the future path-aware Internet.

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