There would be many drawbacks to learning such terminology for those interested in NT Greek.
1. Names for months differ in different cities--and almost never occur in the NT. What use would it be to know that a month had the name of elaphebolion? 2. To learn the names for different vessels in use in a household, e.g. krater, amphora, pyxis, etc. would contribute nothing to NT studies. It might make sense to learn the difference between kore and korasion. Numerals occur rarely in the NT.
3. Does one need to know what a thiasos is to appreciate what an ekklesia is? I doubt it.
In short, the practical thing to do is teach the vocabulary that actually occurs in the NT. If one learns about 900 words, all that occur more than 10 times in the NT, one can read 90+ percent of the NT text. Of course, one needs to know the principle parts of verbs and noun/adjective declensions. Most NT introductory texts do not teach the optative, since there are only a small number (67) in the entire NT. When I learned Attic Greek, I had to learn optative forms as well ad dual forms.
Prof. Emeritus of NT
Lutheran School of Theology at Chicago