this means and become the only supplier to the EU, it could cause a big deal between the US and Russia. But the question there will be; can they risk it?
I feel that you've left whole Arabia out of equation.
While the Arabs are extracting big time (they do need the money for developing), US tends to keep reserves, as you said, for generations. Keep in mind that it's not only cars, trucks, ships, planes need oil. Keep in mind that your clothes also contain a fair share of oil-based products, and it's just an example. US will keep its industries going for long.
So I don't think that US will become "the only supplier of oil for EU". At least not for long.