In order to have free trade with Taiwan, Japan, Singapore, etc. US is using their military force to contain China. In order to do so, their military forces have to be superior to China's. If EU wants to "go alone" and not rely on US power, they would need to do that themselves (or be content to not trade with a lot of the world, where they cannot project military power).

Same with Middle East. Clearly there are competitors for local energy resources - e.g. Russia, increasingly China as well - as well as tensions in the region (e.g. Iran vs Saudi Arabia). EU depends on that energy, so protecting it is a matter of "national security". Currently, EU is relying on the US to maintain that.