And Cromwell did.
I don't mean to discount your comparison; religion is the subtext in everything that happens in the Middle East. I just don't think the West has the religious critical mass (pardon the pun) to mount a crusade again. And I don't think Islam has the cohesion. So it's a matter of apathy versus chaos.
At least at the religious level ...
Whatever the West is fighting for, it isn't Christianity.
However, there are many parallels.
One I find intriguing is the eventual requirement to separate the warring forces, as much as possible, into 2 separate nations.
Cromwell did bring a religious element in with his, but we could say that the US is bringing a political element in that is at odds with the religious history of Iraq. The democratization of Iraq is a contrary doctrine to Islam. This democratization is a matter of faith.....that all the world would be better were it democratic.