Democracy has not failed because a minority are unable to get their unpopular views reflected in policy.
Extremists have always responded to that fact with violence, but I did not expect to see that response proposed here.

us whose governments involve us in organised slaughter in distant countries
If a majority believed that, the government would fall.
They don't and nor do I.

The slaughter in those lands is overwhelmingly committed by others, who happen to be Muslim.