This is the response I've received when asking why the race seemingly stopped at the moon landings rather than continuuing on to other planets and moons.
Frankly you've got it backward - ICBM's (technically the rocket stages of them) were use in both the Mercury (Redstone and Atlas) and Gemini (Titan II) programs. These were based on ICBM's that were already operational. Their ability as ICBM's had already been demonstrated by their test firings. The Saturn series of rockets used in the Apollo program were designed for that program, and never served or were intended to serve as ICBM's.