It may devolve into a war against a particular mindset.
Fighting WWIII would be better.
"We can cure pneumonia,
but not a cold."
I think not. Your approach reminds me of the defeatist, "Better Red than dead" crowd of the '50s and '60s except that your approach is exactly 180 degrees to the opposite extreme.
We won the cold war not with WWIII but with a better set of ideas and a better economy. We didn't go Red and we didn't go dead.
Islam is NOT the enemy. WWIII is NOT the solution.