On the simplest level, you are right. Not that I'm abandoning reason myself, but I think you're being too rational in analyzing the threat.
We don't have unlimited license to kill our enemies. Quite the contrary. Our desire for victory is very, very weak. We want to win, sure, but we don't want anyone to get killed, and we don't want to break anything, and we'd like to keep the costs down, and we don't want to offend local sensibilities, and we'd don't want to look mean to the Europeans etcetera etcetera.
In contrast, the jihadis belief that killing children who accept candy from American soldiers pleases God, and kill them without remorse. Such men require absolute strength of will. In a world full of cowardice and humiliation, men like that become heroes. Americans have a hard time thinking in these terms, but we need to start understanding this strangely resiliant threat. We dismiss the power of religious fanaticism at our own peril.
As for the "we" that you think has little desire to win, I don't see it that way. We have some weak domestic enemies as well as some weak foreign enemies. Their weaknesses are of different kinds, but both are hopelessly weak. Our domestic enemies indeed want to do as little as possible. But that makes them quite unformidable as enemies. All that is necessary to defeat them utterly is to ignore their bleating, since by their own admissions they will never actually get off their asses and do a darn thing to us. The foreign enemies are perfectly willing to get off their asses, but weak in every other respect and readily annihilated.
What neither possesses is the simultaneous willingness to act with such restriction in the aim of that action as calls forth numerous allies and steady will. There is a reason justice is the settled policy of all the greatest political powers in the world. It simply generates gobs more power than desparate spasms of ruthlessness.
There is no power in ruthlessness. It is superstition to look for it there (the violence to conscience involved is experienced as overcoming the enemy, when it has no effect on him whatever). Look at the most ruthless parts of the world, and you find division and squalor. Ruthlessness as a road to power leads to Somalia - starving gangs of hoodlums fighting to the death over the last sack of rice somebody better dropped before leaving. Or the Congo - famously the greatest power of our age (sic) because all sides are willing to eat one another.
Meanwhile, where principle dedication to worthwhile cooperative efforts are the norm instead, you find not absence of will, but Marines, steadfast beyond the dreams of fanaticism, armed with actual honor, covered in glory, surrounded by the buried empires of superstitious ruthlessness they have annihilated - and also armed with the technological marvels the author foolishly slights, which our actual enemies would give their right hands to have a tenth of.