If the EU creates a strong military independent of the US, it will naturally push for more autonomy and develop aspirations of expanding its sphere of influence outside the continent. This will undermine the global power structure that currently strongly favors the US. As a hegemon, you win more resources and power by dominating the EU completely rather than allowing them to become another rival to your power. If you don't want global hegemony and the privileges and responsibilities that come with it, just fucking admit it. You can't be a global hegemon while isolating yourself from the entire globe as you actively antagonize it and beg for someone to replace you. China and Russia are already attempting to do this, and you should not add the EU to that mix. They are currently a captive, highly-developed consumer market for the US which is entirely dependent on you in terms of the military and increasingly energy. Again, why would you antagonize your cash cow? Do you seriously think that the life quality in the US will improve if the EU and China deconstruct your hegemony and become independent powers that you just cannot fuck with without any consequence?
I don't think "Europe" has the potential to become a military competitor to anyone in the mid to long term, because unlike the US or China, it's not a unitary power, but a loose collection of more than two dozen independent countries. The degree of cooperation and integration they achieved is unique in the world and downright miraculous, but I see no appetite to confederalize the continent, and without confederation, there's no way member countries will agree to hand over control over military or foreign policy off to other countries.
You also need to keep in mind the primacy of domestic politics over foreign ones. Electorates don't really understand or care about the mid term implication of international crisis, but they will absolutely vote for insane demagogues over a 2% tax increase. Even if not spending 200 billion now to fix a problem will mean they need to spend an additional 5 trillion over the next 20 years to manage it.
I think the most probable positive outcome is the formation of cooperative blocs within the EU for purposes of self-defense and some small scale interventions Europe's periphery.
I haven't read much of anything about Chinese goals in Europe, so I wonder whether they're making offers to build genuinely mutually beneficial relations, or only to divide the West, or both, or some other thing that doesn't occur to me.
I personally think Chinese expansion in the Far East is a bad thing overall, but I also think Europe has no way to meaningfully affect outcomes there, and should thus not alienate the Chinese over it.
I think Europe is a far more important partner for China than Russia is, but arguably a less reliable (due to free elections) and less comfortable (due to civil liberties) one.
China could be an interesting new partner for Europe if there was a way to bridge differences. I wonder to what degree those are caused by European alignment with the US anyway.
