Well you'd need a lot more than an Internet independent of the US. The same US cultural influence was prominent before the Internet became popular. You'd either

Well you'd need a lot more than an Internet independent of the US. The same US cultural influence was prominent before the Internet became popular. You'd either need a new super popular language apart from the globally popular English, and or you'd need English to decline substantially (this would decimate the US cultural output/reach/influence). It's worth noting that a variation of language collapse may be occurring. The English speaking part of the US is imploding (aging demographics, fentynal, Covid, mediocre healthcare for the bottom 1/2, etc), the Spanish speaking part of the US is rapidly taking marketshare (immigration being the only thing keeping the US population afloat). You can expect some decline in US cultural power accordingly, as Spanish is less popular globally than English (and far less potent as an entertainment, media force). The EU will indeed end up more or less making their own Internet. That's happening gradually. Their own rules, laws, beliefs are increasingly governing their slice of cyberspace (and anything in tech broadly). That separation will only get wider. Over time, the laws governing the EU Internet end up making it quite distinct from the US Internet, from the Chinese Internet, from the Russian Internet, and so on (as different as the physical spaces are today, at least).