I'm not claiming it wouldn't have happened, I'm saying in a two party system the electorate can't punish them for this decision to go to war (UK case), or for anything else the general public thinks were bad decisions. So the two parties end up being nearly unaccountable.
Also, the two parties tend to stand for such a broad range of issues, that it's very difficult for the electorate to express what they find good and bad in them. With a coalition government system, if there's an election, and a single party of a coalition takes a hammering while the other parties in the same coalition improve, it gives a much better hint at what the electorate is unhappy with.
I see it in terms of a spectrum with direct democracy (ancient greece style) on one end, and oligarchy or dictatorship on the other end, with the government systems we're discussing somewhere in between. I believe "FPP"/two-party systems are much less democratic and aren't kept in check as much as coalition governments.
Now democracy is a means to an end, i.e. good governance; and if a bit less accountability and more concentration of power leads to better governance, then fine. But that's not what I'm seeing from where I'm sitting. Your claim is that two party system is pandering to the middle. But the way I see it is that the middle is dragged to wherever the two parties want to take it - because the middle has no choice in the matter anyway.
It's my impression that "the middle" in the US seems far more on the right than in a lot of other parts of the world. Is it because the US people are inherently more right wing, or because that's where the two parties went, and for lack of choice the electorate followed?