That's the thing, Americans have become very skeptical of our own influence and power, for good reason. Look what we did to the Middle East. Look at the shenanigans we were funding with USAID. There isn't actually a constituency for this imperialism stuff in the US. US voters don't like it.
In any case -- if we had so much influence, why were previous presidents like Bush and Obama unsuccessful in influencing the EU to fund its own defense?
>forcing the EU to become a competing military power
It's not about competition, it's about Europe taking responsibility for itself.
You want a global cop? How about you do it yourself for a bit? It's a terrible job. Maybe you should take a turn at it.