This means that opting to go America-free in terms of international commitments might by the same as becoming trade free regarding the level of external contact outside of the EU that currently exists. Perhaps that's okay and even a desirable outcome, but it might behoove us to look first and see what kinds things that we do actually like in the world today might not exist were it not for the sizable commitment made to international institutions by the United States and that might then have to be replaced by someone else if the US was to reduce its provision (or capability) of providing them.
At the very least, with the threat of expanding additions of carbon and greenhouse gases by non-OECD countries, a means of asserting and compelling international commitment outside of a narrow EU region are probably necessary for the well-being of the EU.