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

[Rongway]

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.

More likely, it was a future-proofing precaution just in case such a gear upgrade ever caused the gear to increase in level, making the new gear unequipable. Currently no gear upgrade methods change the equip level, but these devs would have considered that even if they deemed it unlikely to ever happen and decided it would be safer just to disallow upgrading equipped gear than it would be to put in a bunch of unnecessary checks to cover scenarios that might never happen.