A young girl is thrown out of her daily life when she wanders into a supernatural world and facing hardships, grows with the help of benevolent older figures and finds that she actually possesses the strength to overcome them.
As you rightfully pointed however what distinguishes Spirited Away is how original and evocative its setting is. Miyazaki is a master at reframing common experience in enchanting way. The train is a good example. Anyone can relate to the fear of taking public transport alone for the first time, being surrounded by stranger, having to use a ticket but in the act is both stripped to its bare essential and yet shot beautifully.
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.
With that said, I don't think Chihiro needed to know where she fit in the past, because, as she and practically every spirit knew, neither she nor her parents belonged there. Her parents, in the context of the story, weren't her connection to the past either, but to the future. At the beginning of the film, her parents were much more enthusiastic about the future (i.e. moving) than she was. Rescuing them wasn't about keeping her progenitors alive out of filial duty, but about rescuing her and her parents' collective future to live freely as human beings.
The only direct connection to Chihiro's past (established through a beautifully done albeit unconvincing Deus ex machina) is Haku and he's the one who later tells her to move forward. I'm not sure what class of spirit Haku is aside from being a river spirit, but almost everyone who operates the bathhouse, including Yubaba, are yokai and it seems they're lot in life/death is to keep the bathhouse running for eternity without change or reprieve. The yokai either don't have agency to begin with or trade what agency they have to remain perpetually employed. Chihiro, on the other hand, possesses and develops her agency as she tries to find a way to rescue her parents.
In addition, "senseless obstacle jumping" an apt description for what Chihiro had to go through . Various mythologies often depict the gods and spirits of nature as capricious as they are mighty and skillful. I suspect that Japanese kami/yokai are no different: to be revered but also cautiously interacted with, if at all, lest you invite their more "playful" nature.
her self discovery is certainly initiated by an uneasy transition point in her life (moving), but i'd argue that geting beyond that discomfort is not the main point of the movie. and for sure, the spirits are mischievous, but they all carry their own baggage that they try to dump on her (sometimes literally), which is what she's directly and figuratively resisting via all the hoop jumping. she's picking and choosing who she's going to be based on what her ancestors (loosely speaking) are trying to foist onto her. the yokai[0] are stuck in the past but she's not, and she must move beyond her ancestral past to escape back into her real life (which is symbolic of her forming the kernel of self identity). this is where your point about the future (and moving forward) dovetails nicely.
in that way spirited away is a story about a young human going through the process of realizing that they are a self-aware and self-actualizing person destined to become an adult (who much couch themselves in family and tradition), and not simply a child who can play and not care about the world (and her parents especially) anymore.
[0]: it's neat to see the parallel with yaoguai, which is the chinese version of these little demons/goblins, as i've more recently been watching wuxia/xianxia dramas.