OP you said it yourself that your issue is really with the FATE grinding, and that is a perfectly valid point, however I would only say that compared to previous relic weapons, the Resistance Weapons are far more palatable to "grind", and the playerbase seems to mostly agree.
The idea of possibly giving an alternate route of getting the needed items via dungeon running isn't a bad idea though, but I guess the question would be what types of gameplay and engagement were the devs aiming for when they designed it the way they did?
I can see a thought process of perhaps not wanting to make it primarily dungeon based, as it could possibly result in lots of dungeons being speedrun at a pace that many would actively dislike.