If you go back to the decades in which the US became the world hegemon (post-war era) the difference is way more stark. It's not that the EU resigned - it's that the US muscled them out!
One theory is that in Europe in the 1980s, workers became so much more empowered that the private sector lost the will to invest. Start with https://delong.typepad.com/kalecki43.pdf for the basic concept here, but there are many more examples.
A VAT-funded balanced budget welfare state is a purely redistributional mechanism which, while great, is not sufficient to undo this sort of thing.
Direct government spending like the military sort is a way around this. Maybe the workers are militant, but will the democracy just allow itself to decline military because you don't feel like dealing with that?
Workers vote too, so I don't think so.
I think the US is a very weird state - it's probably the most consistently old-school liberal state in the world, it has negligible worker activism, colossal natural resources, and its position as world hegemon gives it all sorts of non-imitable economic advantages. I don't think you can copy the US if you're not the US - the closest in terms of economic policy is the UK, and the UK economy is kind of like a corpse in a bin bag.
The EU is barely a confederation, let alone a federal state.
Is how a military industrial complex starts. Then it seeks to justify its existence by either meddling everywhere.
If people simply don't need jobs as much, on the margins, it's much easier to have healthy conversations about what investment is actually good, vs what is just make-work or worse.
There is no inherent weakness of Europe. It has far more people than the US. All that welfare state makes it far more efficient too in many matters.
A little "Military Keynesianism" would, frankly, be really good for solving Europe's problems of higher unemployement and whatnot too. I am generally against such things, but the welfare states make the risk of runway jobs guarantees and military industrial complexes less bad.
In general, Europe missed out on Keynesianism it seems (the military or non military varieties). 70+ years of welfware states is being undone by stupid austerity. They figure out how to be good to the poor (unlike US) and not do austerity (like the US, despite what you may think), and they should leap ahaed of us.
The "US-lead world order" is Europe's choice.