There might be some argument to change the classification of some roads. Teryan and Koghbatsi Street might serve more for the purposes of “through routing” and the difference between those and surrounding tertiary roads could be negligible (https://yandex.com/maps/10262/yerevan/?l=stv%2Csta&ll=44.511310%2C40.180290&panorama%5Bdirection%5D=223.024197%2C-14.750631&panorama%5Bfull%5D=true&panorama%5Bpoint%5D=44.511129%2C40.180111&panorama%5Bspan%5D=94.719955%2C60.000000&z=18). Spendiarian Street and Hin Yerevantsi Street are more localized relative to tertiary roads such as Pushkin Street, which is why those were modified that way. Parpetsi Street might serve as an artery that direct drivers to Pushkin Street, though it is hard to evaluate because of surrounding residential buildings and road width.

Having a consistent road hierarchy is sensible, though we are in agreement that function plays a role in determining classification. Ultimately, editors and communities have different interpretations for highway classification, especially when the difference is small. I hope my explanation for these individual highways is helpful in determining the most optimal decisions for your community.