The survival of socialism even after the defeat of the champion of socialism, the Soviet Union, should remind us that defeating the jihadis won't kill the idea of jihad.
But we should also not forget the benefits of defeating the champions of an odious ideology that would kill to put you in paradise on Earth against your will, even if the odious ideology lives on in people too stupid to benefit from a beating with the clue bat.
We are better off with socialism or Islamism that doesn't have a champion who will try to kill us to make their ideology real. It is sad if people live under those regimes, but not our problem, really.