Totally agree, but the problem is it’s hard to teach, and there are many different viewpoints, and teachers don’t want to attract controversy.
Or teachers may not know what to say, since this is very personal. For example, someone wrote an article about how R’ Yosef Ber Soloveitchik was a very spiritual person and felt the presence of Hashem, but he rarely talked about that kind of thing publicly.
Ideally, people should be taught about how to cultivate spirituality, from talking to Hashem in your own words (especially associated with Breslov, traditional Jewish women’s prayer) to meditation (Chabad, kabbalah, Meam Loez) to always reminding yourself of Hashem’s presence and trying to feel it in your life (Bilvavi — a sefer you can read for free in English online, by the way). There’s an encyclopedic book on this subject, Jewish Spiritual Practices. But I personally have gained a lot from the R’ Arush books.
Yes, we need a balanced education — Gemara, but also halacha, hashkafa, mussar, chassidus, history, etc. People need to understand that many people will not be happy and fulfilled in their Avodas Hashem until they find something that really works for them or inspires them. It doesn’t have to mean changing one’s community affiliation or anything — there are certainly Litvishers who learn chassidus and sephardim who learn Litvish kabbalistic seforim and so on.