The Kabbalah should be part of contemporary Jewish teachings because it has a lot of important information in it. It teaches about mysticism and spirituality and not so much about religion. This is great for helping Jewish people and others understand their place in life. There is so much to the Kabbalah that it should definitely be included.
Kabbalah, or Jewish mysticism, should be more mainstream and is definitely a part of Jewish tradition. As such, rabbis should be able to make Kabbalah part of contemporary teachings since having a person relationship with G-d's spirit should be relevant to contemporary Jews. There is nothing wrong with having a closer connection to G-d's presence in everyday life beyond reading the Torah and going to synagogue every Friday and on high holidays.
The strength of the Jewish community is history. While faith can be cited as a pillar in their temple, knowing why things are done a certain way is the key. Why is Hanukkah important? What do the candles mean? The Kabbalah should be included in contemporary Jewish teachings in order to impart full disclosure on their history. To not include it would be rather blasphemous.
Kabbalah is not part of contemporary Jewish teaching because it never has been - its a 500 year old sub section of a several thousand year old religion, and has far more basis in esoteric and hard to understand topics than anything that might be applicable to people's daily lives.
No, Kabbalah should not be part of contemporary Jewish teachings, because it is not part of traditional Jewish teachings. Kabblah is to Judaism what the universalist church is to Christianty. Technically they call themselves Jewish, but they vary a great deal from what Judaism teaches. Those studying Jewish teachings should learn traditional Jewish teachings, not variations.