I agree that alignment locking is not the usual for D&D. You don't really want to do that too much because you want players to be able to use the weapons they find.
However, you don't specifically call out that a weapon belongs to a particular god and then not restrict certain people from using it. For example, you would not let Shadowheart use a weapon blessed by Selune because she is a cleric of Shar, Selune's mortal enemy.
I could see Everburn not being alignment locked. Maybe Zalk acquired it from somewhere and it isn't a devil sword. However, The Sword of Justice should be locked so that certain types of people aren't able to use a weapon that is specifically Tyr's - King of Good Gods. Someone like Astarion should likely not be able to use it even if they had the proficiency.
This is part of the reason I want the alignment system implemented. It just doesn't make sense to allow someone of a good alignment to be using something from an evil alignment or vice versa.
Yet there IS a Selunite amulet in the game that Shadowheart can use and the only thing stopping you is RP. Also, no one said the swords in question are sentient or have any alignment of their own. Just because a paladin slays 1,000 demons with a sword doesn't make it "good". Simply being associated with a deity doesn't confer alignment. Alignment has virtually nothing to do with 5e from a mechanical standpoint.