It seems the language is changing with millenniums and technology. Using the full negative was always taught and spoken. Je ne sais pas....
However, more than ever now, the language seems to be going towards shortening answers or verbiage with less words. For example; Je sais pas. I have never taught this formula and insist that my students learn the full "je ne sais pas." However, you are correct that when expressing short answers, it is becoming more common to say: pas toujours, pas vrai, pas possible, pas souvent.
I have never seen it in writing. It is only in spoken French that it is becoming more and more common to abbreviate or shorten sentences. I now encounter everywhere "prof" instead of professeur. However, it is rare that you would see the abbreviation in written material.
It all depends on whether you are speaking and want to be part of the new way of abbreviating, or if you want to learn the old school French the correct way.
Hope this helps,