I am not sure it is about fighting. We win fights almost effortlessly, even despite doing so with 9 fingers tied to our feet. The problem is their approach to "state building"; part of it is scientific and part of it is ideological.
First, the scientific - they believe that everyone is fundamentally not just the same biologically, but the same in terms of values, desires, and aspirations. The social democratic state is not used everywhere, but only because not everywhere is as advanced as the West. Once a social democratic state is established, it will flourish and endure forever, just like in the West. Ideological differences with the West will vanish.
It should have become clear this was false after observing 10-20 years of post-colonial Africa, Latin America, India, or at least the fake democracies of far Eastern Europe. But it has not. People believe, quite genuinely, that once girls go to school Islam will wither to a husk as Christianity has done in the West. Even if those schools are teaching that the Koran is the sole indisputable truth and the Mullahs are a greater authority than the state.
The Taliban insurgency will last forever not because we don't defeat them in fire fights, but because we permit the whole mechanism of indoctrination and recruitment to continue even on the ground we have captured. It doesn't exactly resemble those processes in an industrial state, so for the most part we don't even see it for what it is.
The second is ideological. There are certain beliefs that will prompt the current governing class to purge the unbeliever with fire and sword, Islamism just isn't one of them. Putin passed a law to stop people promoting homosexuality publicly. This sparked outrage, some argued even a rekindling of the Cold War. Even in this country one can lose one's job for being critical of homosexuality. But
executions for apostasy are just "controversial", and anyway part of a proud anti-colonial tradition.
There's simply no desire to see crimes committed in the name of Islam in the same light as crimes committed in the name of Naziism. That's just the way things are done there, and anyway, if they'd kept quiet about it they would have been ok, if indeed they didn't deliberately provoke the state to bolster their asylum claim... An attempt to squash out Islamic theocracy in a conquered country would not attract the moral legitimacy at home needed to conduct a thorough de-Islamification on par with de-Nazification.
The conclusion is that the West cannot defeat Islamism by military means and even the local benefits of our military actions are likely to be nugatory, despite the enormous expense required to minimise casualties to a point where they are tolerated at all. I suggest a more appropriate strategy would be to set up an analogue to 'Radio Free Europe'; some kind of 'Radio Atheist Middle East', but more subtle than that. The military battle cannot be won without first winning the ideological battle.