Uhm... no? If there was no EU, we'd now have a lot of bilateral agreements between the US and single European states, with each individual agreement consisting of 90% what the US policy makers want and 10% what the country's policy makers want.
The only reason that this takes so long is because the EU is actually large enough to put up some resistance. Every individual country, including my native Germany, would have been steamrollered by the US.
Just look at the bilateral treaties that EUropean countries have with the US. They are always really lopsided, like that one where the UK extradites its own citizens to the US, but the US doesn't reciprocate.