I just realised military buildings like barracks in regions that are not the capital of a province serve hardly for anything as nly the capital's modifiers to experience seem to be used when raising new units. Maybe the province's port if the capital has none also plays a role when building ships, hae-ven't tested that yet.
Anyhow, would it be possible to add something so that non capital regions will at least contribute a bit (half? one fifth?) to experience of units raised in their province? Otherwise there hardly ever is a point to building those or in keeping one's captured from enemy civilisations.