Discussions elsewhere suggest that this happens and that smaller moons would tend to low inclination with respect to the planet's equator faster than larger ones.
For example, Mars' small moons are inclined only by 1° or so while Earth's moon's inclination varies between 23-5° and 23+5° with an 18.6 year period.
But this is not a good example because the origin and history of these moons is very different.
Question: So if we had two Earths around two Suns at 1 AU each, and each had a rocky moon like our own inclined at say 10° with respect to the Earth's oblate equator at the same distances except that one moon was big and one was small:
- Would they migrate to low inclination over time?
- If so, does the time it takes depend on the Moon's size?
- If so, which would tend to migrate to low inclination faster?