I take your argument at face value (in that I take it that you believe the EU has that goal at some level). I just to not expect it, as an organisation, to consistently promote that goal (for much the same reasons lots of countries fail to serve their citizens).
Profit making businesses have the explicit goal of making shareholders better off. Management usually choose to balance this against other goals (ethics, the good of wider society, their own interests...), just as the EU has the explicit aim you state, but, similarly, has other conflicting aims.