The more I think about it, the more I think that subsidiarity is emphasized within Catholic Social Teaching not only because it is a sound political principle, but as a reminder to the secular rulers that they should be prudent and not over-extend themselves in their legislation. It is a more pragmatic approach to over-sized polities, to the world as it is, rather than focusing on claims of justice and rights, which may be true but will nonetheless be ineffectual, given who has power and the inertia of political culture.
Is it true that the Church would sympathize with those who aspire to a more humane political arrangement, appealing to rights or self-determination or secession? Where is the balance between obedience to a legitimate authority (poorly exercised) and political reform (or even dissolution) to be found? In the impact upon the common good.