Why is this specific mechanic during Relics Quests still that way?

[Daeriion_Aeradiir]

It is due to the fact that, in the back end, you don't upgrade the weapon, you delete the weapon and then put a new item in the player's inventory, this is also why materia is not preserved. If you had the weapon equipped, there would be a point where you character has nothing equipped to the main hand slot, something that is not normally possible at all. As for why they cannot just replace the weapon in the same slot, I suspect it has to do with new items not being able to be directly equipped to the player and it has to go into the inventory.

There is a bit of technicality behind this answer - there actually is a hidden "job" that NPCs get assigned when they aren't battle related NPCs, along with a potential catastropic glitch that causes the player character to not have a weapon equipped - "Adventurer" (ADV) : https://www.reddit.com/r/ffxiv/comme..._0_adventurer/, so removing a weapon from the player character actually doesn't cause any issues, as long as they get re-equipped with a weapon before control is returned to them. (This actually happens in some other cutscenes when the player equips prop items for the cutscene)

Theoretically speaking, they could code it so the player character in the cutscene is assigned to adventurer temporarily for the duration of the cutscene, then re-equip them back with the new weapon, but that's on a thoeretical level - there's likely some other problems or unseen control variables in how quests that require specific jobs function in the backend, like Rongway mentioned with the potential 'gear could have leveled up' idea the devs may have thought of long ago.