>As of now three leading powers exist: USA, China, Russia
Aren't you forgetting someone? Europe united into a (con)federation would have more military power than Russia and China and would rival economies of USA and China. I mean, they are not a "leading power" right now, but out of the three you mentioned only USA can be truly described like that.
So, a united and independent Europe has the potential to be more of a rival, a threat to USA dominance than Russia or China. Only if the latter two would combine their potentials in a firm political and military alliance akin to NATO, only then would they be able to rival USA or Europe (think like - "if USA attacks China Russia will launch all their nuked towards USA, or if Europe would attack Russia, China would send all their ground and air forces to the European front to fight alongside Russia"), which is of course highly improbable.
Therefore it is in American interests to keep Europe from further integrating into a single country (ergo "Brexit"), and to keep China and Russia from entering a true alliance. USA will try to keep Europe dependent both on American resources (instead of, say, Norwegian gas and oil) and on American military might via NATO. To this end they'll maintain Russia as a threat to Europe and the raison d'etre for NATO - a source of threatening newspaper headlines, but not much of a real threat. They will also try to deepen the rift between the "old EU" and "new EU" (ergo Visegrad 4), perhaps helping Poland to become a rival of Germany and the power center of [s]Eastern[/s] sorry, Central Europe. Meanwhile in Asia (and Africa) all their might will be poised against China. May be we will finally see something of an asian NATO - NEATO, if you will.