Does tidal locking also slowly reduce the orbiting body's axial angle? The Moon is tidally locked to the Earth, and it has an axial angle of 6.687 degrees relative to its orbital plane. I'd like to know: did the Moon start out with a higher axial angle?
In other words, does the process of tidal locking also slowly reduce the orbiting body's angle of rotation? If so, how does this work? And will it someday cause the angle to be reduced to zero?
A secondary question would be: suppose an orbiting body had an extreme axial angle, say 80 degrees (perhaps due to an impact during its formation), how would this affect the process of tidal locking?
In general, tidal forces will cause the obliquity to decrease for an initially prograde rotation, so unless something is acting to disrupt the situation you would expect a tidally-locked satellite to end up with a very small obliquity. This is the observed rotation state of most of the major satellites in the Solar System.
The Moon is something of a tricky case thanks to its location and its history of outward migration. The Moon likely formed close to Earth in a near-equatorial orbit. As it moved outwards it crossed the Laplace radius, which marks the region in which the Laplace plane (the plane about which the satellite's orbital plane precesses) transitions from being aligned with the planet's equator to being aligned with the planet's orbit. If the Earth was originally in a relatively high-obliquity state, this transition would have resulted in rapid changes in the Moon's orientation, and the Earth's obliquity becoming more similar to its present-day value.
The upshot of this is, even though tidal forces tend to damp the inclination with respect to the Laplace plane, the Moon's orbit is still inclined by a few degrees to the Laplace plane (likely as a result of picking up a fairly high inclination during the transition across the Laplace radius), and the nodal precession has a timescale of about 18.6 years. This timescale is more rapid than tidal forces can decrease the Moon's obliquity, so the Moon cannot evolve into the zero-obliquity state.