It seems like (other than Chabad) most people do not say Al Tira at the end of davening - they finish with the end of Aleinu/V'Al Kein. Is this an error or is this intentional? If it is intentional then why do we skip it and why do the Sidurim print it?
First you need to determine if the original custom was to say it at the end of Aleinu in the first place. There is an article on exactly this subject in Hakirah (Vol 10).
It is really hard to determine what is an error when dealing with an area that is primarily down to Minhag. For instance, in the case at hand, the oldest siddurim(those of Reb Amram HaGaon and Reb Saadia HaGaon) end with Aleinu, as does the siddur of the Mekubalim, and the actual siddur of the Arizal(which was recently published in photostat with facing pages in modern typeset but unfortunately currently found online).
However, for reasons not entirely clear, the Hida added the posuk of Shema Yisrael after Aleinu, and this was primarily adopted by Sephardim.
When exactly "Al Tira" was added to the Ashkenazi siddur, I am not certain. However, like Piyyutim and other things it would be more a matter of individual communal practice. Most modern Siddurim are no longer published by their individual communities, or for individual communities, most are not published to meet the largest possible population, and thus often include things normally excluded by some communities. For instance every Sephardi Siddur has Lekha Dodi as part of Kabbalat Shabbat, even though a large portion of the Sephardic population never says it.
It is not written(to my knowledge) in the Shulhan Arukh to say Al Tira, after Aleinu, so I am going to say that it is a minhag, and thus it is not an error to skip it, but neither is it an error for Siddurim today to be published for with inclusiveness in mind.