https://www.euronews.com/2018/05/02/which-country-spent-the-most-on-its-military-in-2017-
https://www.atlanticcouncil.org/blogs/new-atlanticist/here-s-why-the-united-states-needs-nato
Europe invested €282 billion in military in 2017. That's less then the US but more then China ( $228 billion (€188 billion)) and Russia ($66.3 billion). That might be considered peanuts for a country who seems to be in constant war but its a hell of a sum for a continent whose army would be utilised for defensive purposes only.
So what happens if the EU decides to organise themselves and kick NATO out? Well the US would lose valuable military bases which would make missions spiral out of control. But that's not all. The US would also lose powerful allies as well as Europe would finally be in a position to take foreign policy seriously. For example what happens if Europe decides to mend bridges with Russia? They are our neighbours after all which puts them in a good position to understand the geographic challenges we face. They are also our main suppliers of gas + lets face it their country served as the main graveyard for both Napoleon's and Hitler's armies. Also what would happen if next time the US decide to bomb the shite of a country which surprisingly always seem to be a neighbour of ours rather then theirs and Russia, China and the EU says no? Would there be sanctions? Not to forget that there's that little thorny issue regarding world trade and the dollar. God forbid if lets say the big 3 out of 4 decide to ditch the dollar for foreign trade. That would destroy the US economy.
So you see, the US needs NATO far more then Europe does. No wonder why orange hasn't pulled the plug on NATO as he promised he'll do.
However that's not really the issue here. In reality NATO isn't fit for purpose. Sure its got the firepower to bomb the shit out of Russia however most of its force is deployed elsewhere. In an event of an attack it would take NATO ages to organise itself. Russia on the other hand, being one entity, had been far more efficient in spending wisely its resources. I am no genius about this but from what I heard from military veterans, its military had been built around quick deployment followed by lightening strikes. The fear is that Russia would gulp huge pieces of Eastern Europe then threaten with nukes if it ever gets attacked. In that scenario May/Trump would have to choose whether they would sacrifice lets say Talinn or risk enjoying a nuclear winter in London or New York.We all know what they would choose.
The EU army would give Europe the independence it needs to shape its own foreign policy. From a military point of view + it would also reduce redundancies between respective militaries and it will help the continent build an army suited for the threats Europe is facing.
Please click on those links as you'll get pretty much most of the information from other sources