I might be mistaken, but as far as I remember, there were NATO troops (that were not US troops) in Afghanistan, for decades, not because any European country declared war to Afghanistan.
I am not expert in history, but I cannot recall Europeans using US troops in an active war since creation of NATO. The opposite can be said in this century, though.
I do not deny that having the back of US, that has possibly the biggest military in the world, is favourable for European countries.
But I am absolutely tired of this discourse that NATO only benefits the others, and that USA doesn't get any benefit from it.
It is beneficial for all parts, and that is the reason it is an alliance. And USA has used it for its benefit for quite long; thus, it is not unreasonable that allies might rely on its help.
Besides, it is beneficial for USA to keep Europe stable and in peace — most clearly, for macro-economic reasons.
