What would be the practical consequences (on earth) if the Moon was not tidally locked? I was thinking about the fact that all the largest Solar System moons are tidally locked to its primary and this question arose.
If the Moon was not tidally locked, it would mean that the Moon is in the wrong orbital distance from Earth. The Moon is tidally locked because it is close to the Earth. If the moon were closer, it would approach the Earth's roche limit, be torn apart, and its debris would become a ring for ~100-200 million years. If it were too far, it would continue to drift outward until it was free of Earths' gravity.

By being tidally locked, the Moon has been extending the Earth day by slowing down the Earth's spin, to about ~6 hours from an 18 hour day to a 24 hour day. This process will continue into the future until the Earth is also tidally locked with the Moon. The Moon, while in this state, has also stabilized the Earth's seasons by stabilizing the Earths' orbital axis.

Lastly, a possible indirect consequence would be upon human history. Mankind would have probably abandoned the celestial sphere model in favor of the spinning Earth model much sooner had they seen proof that a celestial body could spin and rotate, much like when Galileo saw that moons were orbiting Jupiter.