It doesn't have to do with Goshiki. Goshiki quest starts at the Elder in Raging Tides, the Tideborn King is in the Cloud Temple (above the city, talk to the teleporter in Raging Tides and go to Quest Related where it says "Cloud Temple").
Edit: just checked on my seeker, who does not have the Winter Harbinger quest and never did and he can still get the quest at the Tideborn King, so i'm guessing you still get the item and you can npc it. So yeah, it's something that could use a fix at some point.
Maybe this could be fixed by making the items unsellable+non discardable+non dropable and having to go to the Winter Harbinger and turning in each item one at a time.
This way you couldn't loose the item but you could still have the spots free, not that with 80 spots it'll do a difference xD
Also, the quest is trashable so if something like what i suggested would be done i'd say to make the items go back in ur inv if u did trash it.