Our moon, and those of mars, are special cases. They are most likely the result of collisions involving the host planet and some other very large object. They are bigger and closer than any 'natural' moon formed during the formation of the solar system. So it is expected that they are unsymmetrical both in shape and orbit, resulting in them having few stable orbits for sub-moons. Collisions are certainly part of the equation, but there again many of those collisions were associated with debris from the initial impact that created the moon.

A 'natural' moon formed early in the life of a solar system could be much further from its host, with much more symmetrical gravity and many stable orbits ready to host sub-moons. A moon is also in a much better place from which to capture a passing body.