What extends US law to the entire world is actually access to the US banking system and consumer base.

Unless you think the US is going to go to war with its allies, its military power has little importance in this context. The US is a large, wealthy market for imports and a supplier of many products and services that it exports. It's a huge financial centre. Despite the unfortunate state of its government and public services by the standards of a modern democracy, it's still broadly aligned with other modern democratic nations in terms of values and culture, which means it's still a much safer partner to trade and cooperate with than you'd find in some other large parts of the world.

This makes playing nice with the US a diplomatically and economically sensible policy, up to a point. I suspect the US will find it encounters that point increasingly often, partly because the rest of the world is also changing and partly because Trump did so much damage to international relations and the US may never fully recover. The ongoing negotiations about global corporate taxation are a good if rather dull example.

Yeah, which is why the top comment is talking specifically about companies with no assets in the EU.