This paper performs a comparative systemic analysis between the "Productive Ex-ante" immigration model of Uruguay and the welfare-dependent regimes of contemporary Europe. Using the Theorem of Axiomatic Necessity (TNA), we demonstrate how flow velocity and initial fiscal cost determine long-term institutional stability. While Europe faces systemic stress due to state-mediated insertion and high social friction, Uruguay attracts "low-entropy" migrants who arrive with secured income and portable professions. The study quantifies the "Shock Sensitivity Theorem," revealing that resilience is a geometric property of institutional saturation rather than a result of political goodwill. By mapping micro-behaviors—such as social anxiety levels—as proxies for systemic health, this work provides a deterministic framework for predicting the divergence between sovereign refuge states and failing welfare systems.