The key word here is atm (at this moment, I guess). The problem with military capabilities is that they can't ramp up quickly -- it takes years. Relying on what's needed atm is shortsightedness at very least. Many countries in history paid a very painful price for it, or even ceased to exist. A very recent example is Ukraine. It had exactly the same attitude -- "we don't have enemies atm, why bother". Until suddenly it had.
And the US are not paying $$ for anybodys army. And they know very well how to use their own capabilities outside of NATO and for their own interests.
Because this is the bottom of it. European countries want the protection, while not paying their share, and making fun on Uncle Sam spending so much on their military, and not enough on their social program.
Europeans don't want the US playing global super power. They don't need it. And they ain't paying for it.
[the answer to this question is of course "no", European countries still want the US to be paying for their "protection".]
More military interventions with more refugees arriving at European borders?
There is basically no real threat to European countries atm. Russia is heckling a bit in Ukraine. Supplying Kalashnikovs to separatists and such. But in general, Russia is retreating. With Montenegro joining NATO and things going bad in Syria, Russia is losing access to the Mediterranean sea. And they run out of money quickly!
If things go wrong, special forces (a few hundred men) and French atomic missiles pose enough of a threat for rogue dictators. The large countries can't afford a war, because economic ties are too strong.
Military spending in Europe is exactly where it needs to be. Low. Humanitarian help throughout the world and keeping the inner stability of society (social security, health-care, retirement, ...) gives a lot more bang for the buck. (pun intended)