But something tells me that's not what Europeans generally want...
EU citizens understood and recognize that economic supremacy of some private sector industries is pointless if the gains all go to the hands of a few tax dodging trillionaires with sex trafficking private islands, while the externalities get outsourced to the environment and the public sector to deal with leading to increased wealth inequality, homelessness, crime, drug addiction, etc
That's why they want to see policies that will first address the environment and quality of life, before shareholder returns, even if that makes them less economically dominant.
EU people don't want to live in a world of fent zombies on the streets, cars with smashed windows from petty crime, food deserts, homeless people, all in the name of economic superiority.
Secondly, even if the US as a country is tighter integrated and more financially successful than the EU as a union, the US is not a successful model example of a well functioning society that people in the EU would aspire to emulate, on the contrary, they'd rather preserve the status quo than turning into something resembling what the US has become.