Given a long enough time frame, the human race will either inevitably fizzle out on our single planet, or move on to be an interstellar civilization for at least some period of time.
If the second possibility is to happen, utilizing the moon will most certainly be a stepping stone there. Whether it's covering the surface in solar panels, mining it for helium 3, or something entirely different like simply using it as a staging area for longer range launches, we can't say, but it's virtually guaranteed that humans will be all over the moon in some capacity if they are to expand beyond our planet/solar system.
On another note, the moon is a boring bland rock compared to Earth. I bet the moon is incredibly desperate for us to do something interesting on its surface... "please, let something, anything happen aside from getting smacked with another space rock and getting a 15 millionth identical crater!"