I would argue that's not the case as there are plenty of morally naturalistic European works (e.g. Alice in Wonderland, upon which Spirited Away, among other anime, is based) just as there are plenty of morally didactic Japanese works. The movie may not be as blatant as an Aesop. It's certainly layered with subtext, but it's also a much simpler picture than most make it out to be.
There is a lesson, and it's one given in the form of a command by Hakku towards the film's end:
"Leave...and don't look back."
Chihiro's (and the audience's) lesson is to move forward in life, just as she's done up to that point. If you recall, the movie begins in media res as Chihiro is being driven away from her soon-to-be-former hometown. She looks sullen as she fidgets in the back of her father's SUV while clutching a bouquet implied to have been recieved from a friend or wellwisher in an attempt to hold on to the past. Despite being on the road for at most a few hours, she already misses whomever and whatever she and her parents were leaving behind. She's clearly frustrated by what seems to be an unneeded change in her life.
Throughout the movie, she faces one resentful change of circumstance after another. A change almost always inflicted upon her by an authority figure. As she develops a greater sense of agency, she takes it upon herself to change her own circumstances, and eventually the circumstances of almost every character she comes across including said authority figures.
The point of the movie is that things will change whether it's for the worse or the better, and you can either be swept by the river of events that is life or set your own terms and act accordingly. That's not to say that the latter choice will always bear desirable fruit, especially without a prepared plan. Such a choice can horribly backfire even with planning and preparation. Nevertheless, one should refrain from abdicating one's will in the pursuit of a goal. Instead, one should, inasmuch as one can, choose and direct the path that will take one forward.