"...once we've killed enough violent jihadis to convince the remainder to give up violent jihad..."
How do you purpose that "we" kill these violent jihadis when they're scattered all over the world? How do "we" get rid of the now "American citizens" violent jihadis who have the sympathy of the left wing? (Their oath of citizenship is meaningless!)
More importantly, are we safe in our own country?
Are we (all) safe? No. Will jihadis destroy America? No.