That's a good question, and I don't think you'll find an especially convincing answer.
Polar orbits are "unstable" in a few senses, namely that even in an ideal setting orbital planes will precess around central masses that are lumpy rather than spherically symmetric; rotation of a lumpy central mass introduces further precessions. Nodal precession is pretty interesting, for example. One can concoct all sorts of odd orbital changes by perturbing the rotating central mass "under" a test object in stable orbit.
However, in the case of known solar system bodies, slowly shifting a satellite in near-polar orbit into a near-equatorial orbit conflicts with quite a lot of evidence; by the mid 1960s it was pretty safe to say that known inner moons maintain over very long timescales an almost constant orbital inclination with respect to the planet's equator, while outer moons maintain an almost constant orbital inclination with respect to the invariable plane of the solar system. Interesting exceptions are Triton and Earth's moon, both of which have significant inclinations to their planets. Precessions are primarily driven by the planet for the inner moons, and by the sun for the outer moons.
It's probably worth paying some close attention to Uranus and its known moons (and their formation and/or capture) when considering the various thoughts people have put into the thread. Most of the moons and rings have negligible inclination (i.e., they're coplanar with Uranus's equator), and Uranus's extreme axial tilt is intriguing. If the tilt is because of a giant collision, did the relevant moons and rings follow the planetary tilt? Or did they form in the highly-tilted equatorial plane (for some of the moons), or were they captured into the equatorial plane (for others) post-tilt?