So, I'm having trouble following your interpretation.
The character receives one generally beneficial Essential Trait at either +3 for Minor or +6 for Major, which either positively affects rolls associated with a particular Characteristic in certain situations, like Intuitive +3 or Good Aim +6, or gives the character a beneficial Personality Trait that is part of its essential nature and cannot be influenced by magic (see Essential Traits, below).
If it doesn't apply to just rolls, and instead applies to Totals, A Com 5 Good Teacher with an Essential Trait that applies to writing is writing Q11 or Q14. I'm not following that it only adds +1. It is decidedly not a characteristic specialty, I think you're confusing Essential Virtue with HoH:TL's Mythic Characteristic. Although, I'll note that it says roll for the Characteristic when the specialty applies for the Mythic Characteristic, too. I'll note that there was ample discussion about whether Mythic Characteristic applies to writing, too, with the example for Com being prolific authors. The discussion came up in Doctorcomic's Let's Design a Folio thread and ended up derailing it a bit. Out of respect to Doctorcomic's I didn't engage in the debate there, but I take the same view as ezzelino does.
I'm only exploring the possible implications of making an Essential virtue grant such huge bonuses to writing, and it's entirely appropriate to a thread that discusses an average tractatus quality, since these bonuses would certainly affect what the average is...