The risks are really only economic. And those can be solved with trade pacts... without having to sacrifice any other independence such as with laws, courts, and borders.
I'm from Canada and our economy (and defence) depends heavily on the US, we both strongly benefit from an economic relationship. It's mutually beneficial, as all pacts should be. Yet we don't have to worry about policy being dictated out of NAFTA or worry about the economy of Mexico - which is totally different than Canada - dragging down our own.
Once you look beyond short term economic risks I really don't see thee problem.
It seems to me that smaller countries have the healthiest democracies - one of the reason government functions so well in Scandinavia and here in Canada. The problems with US politics is largely the result of the disparate views of regional communities. Just look at the vast cultural/economic/educational gaps between California, the 'south', or the midwest.
Those gaps are even greater across Europe, so I'm hardly surprised that various countries in the EU, not only people in the UK as we've seen recently, is feeling uncomfortable with the idea. You're just lucky you don't have the Euro to further lock you into the relationship.
Edit: Also the idea the EU stops wars seems ridiculous to me in 2017 given we have NATO and the UN... and that the west only really cares about economics. Sanctions like that were done to Russia or Iran would not last long in a western country, they'd cave in so fast. Pretty much eliminating any risk of internal EU conflict without assuming total economic destruction.