They serve no real operational purpose. Bombers didn't win the war in Korea (stalemate). Bombers didn't win the war in Vietnam (loss). Bombers didn't really participate too much in the Gulf War (win). Bombers didn't win the war in Iraq (stalemate). Bombers didn't win the war in Afghanistan (loss).
You didn't mention Japan. Bombers are useful during wars against enemies with factories, for example China. Heavy metal wars are won by the side with the most standing factories.
At least they "helped" prevent an outright loss...