Just to provide some numbers - the USAF's budget is $170 billion per year. For comparison, that's about the cost of Britain's entire NHS. A very large amount of that goes to airlift capability - plenty of money is spent on air superiority, but the USAF's primary mission in this era of asymmetric warfare is logistical support.
Basically, the attitude of most European governments is "If the US is willing to pay for it, why should we reject their help?"
Probably not that much. We need defense force, we don't need to "police" the world (which really means imperialism). We don't need nuclear capabilities.
Also, the relation between defense and social spending is tenuous at best. Both scale linearly with the size of the economy. Defense spending can actually be beneficial in creating jobs and improving technology.
It's not us you'll have to convince of this, it's your government. They tend to be a bit prickly about such things, no matter how enlightened the general populace is.
The Europeans would have to cut their own social programs if they wanted to do any peacekeeping / humanitarian aid operations - all of that is contingent on American logistical support. Hell, my guess is that they would castigate a more leftist, benign American government; it would make things a hell of a lot harder for a lot of people.
I'm a liberal, and I'd take massive cuts at the war department even without re spending it all on entitlements.
And we don't need such a huge military for humanitarian work either.
Is the cost for that 4.5 x higher than Delta Air Lines annual revenue? ($37.7 billion 2013)
I'm sure most of the cost of USAF is on other things...
The Strategic Airlift Capability has 3 C-17s.
The SAC is, frankly, a symbolic gesture to say, "Yes, we're going to include everyone." The bulk of the heavy lifting is done by standard USAF planes.