I already have Altria Pendragon (Archer) but the rewards are tempting...
If Artoria Archer is already leveled then yes. I mean Kuro doesn't really need that much mats and I'm sure you got everything already, but if Archuria's not max leveled don't. The quest just gives some monuments and five roots, and is intended to be more of a challenge quest to test yourself and like that.
Completing the 100/100 missions combined with the 40AP epilogue quest is good value for the exp spent. That said if you need none of those things no there's no need to ascend Kuro 3 times
It's not like it costs any materials to ascend her, so the only thing it will really cost you is some exp cards. If the exp cards are more valuable to you than the rewards from completing the quest, then don't do it. Otherwise, do it. The crap ton of gold monuments, the spirit Root, and the crystallized lore are probably more valuable than the exp cards, but value is subjective, I suppose.
Think of it as skipping a Crystallized Lore. That's the reward for completing all missions. You do not need to complete the family quest as it does not count toward the 100/100 missions. You can never have enough Lores.
She's very useful against Testament, even at level 60. I cleared it, barely, with two Chloes.
