The question is: Why does the Moon not rotate relative to the Earth? or put another way
What keeps the Moon in synchronous rotation with the Earth?
Is it just a coincidence that the Moon's axial rotation precisely matches its orbital cycle around the Earth?

It's almost as if the Moon was tethered to the Earth by some invisible cord...

Which is exactly what I think is happening... I believe the Moon's surface (either the Dark or Light Side) is magnetically tethered to the Earth's magnetic field, and that it is that magnetic link which keeps the Light Side of the Moon constantly facing the Earth (and the Dark Side constantly facing away).
Back in the 60's I was very interested in the US Space Program. I remember reading one particular report from the Apollo 11 Astronauts where, during their orbital swing around the Dark Side of the Moon, something seemed to grab the Command Module and shake it. They said it felt like they had hit a pot hole in the road - 60 miles above the surface of the Moon...
Subsequent mapping of the Moon indicates that there is a magnetic anomaly on the Dark Side of the Moon.
I believe that it is that magnetic anomaly on the Moon (possibly the result of a large meteor collision) that magnetically locks the Moon in synchronous rotation with the Earth...
Of course, I suppose it could be a coincidence - the orbital cycle and axial rotation just happen to synch up...