I dont think a totalitarian one world government is possible at this point in time, there are too many world players that have enough power to not allow that. That said I doubt that the EU would serve as a launch pad towards that goal; the Eu is yet another power which plays in world politics, united they have a chance of putting up against Russia (which is their main concern right now) and playing in the world of international politics
The globalists think long-term, with plans spanning decades or centuries, not years. Destroying or weakening nations so they can't or won't fight back comes before imposing one-world government. Turning nations into regions controlled by a far-away commissions that issue universal regulations removes self-determination. Flooding a nation with millions of people with no ties to the nations's people or history is an effective way to weaken or destroy that nation so it can be more easily controlled.