Within the EU there is a lot of power imbalance and the periphery gets exploited by the wealthier western nations for cheap labour and resources. National borders facilitate this by being relatively porous for the movement for capital but much more restrictive for the movement of people.

A very good point. This is why formally the national borders won’t be abolished. However de facto centralization and usurpation of national sovereignty, meaning a shift in the power over domestic economic and social policies as well as over foreign policy away from the national governments and toward Brussels, is not at all out of the question. In fact it is already ongoing.

The result of this is effectively turning Europe into an apartheid super-state, where the periphery loses even nominal control over its own policies, becoming trapped in a status resembling an internal colony for the extraction of value and resources. National governments will either be entirely disempowered or national elections will be continually rigged by Brussels, as is happening right now in places like Romania.