Hmm, that is very odd indeed, the game recreates the folder structure for me if I delete the existing folders, obviously also resetting the in-game settings upon doing so. I'll include my .xml file in this reply, perhaps you could use it to force the game to load the file that way if it has proper settings xml structure in it. That being said though, BDO uses EAC (Easy Anti Cheat) to force BDO to run in a non-administrator mode with normal priority etc. by default as far as I know, so perhaps there are still some issues with the folder being read-only and game not having permissions to the settings folder, players usually force priority and other windows options through registries for this game due to that. And having that in mind, even if the attached settings file does get loaded, I'm not sure you would be able to make any changes to it if the game still has permission issues. I assume you have already tried removing read-only from the folders, so unsure what to suggest on that end, but I would assume it has to do with permissions + EAC messing things up.
Also, the game has a "Setting Archive" (top left in settings menu), basically a cloud version of game settings that can be downloaded/uploaded at any time through in-game settings menu. And I suppose you could try forcing the game to save settings by using one of the two custom settings saves (two buttons bottom left in settings menu). But obviously, I doubt either of those would work and actually force the game to save settings as it already tries to do so but fails due to (I suppose) permission issues in windows. So unsure how to fix this, never heard of anyone having similar issues with settings not saving in BDO, but I'll do some research and try to figure it out.
And having said all that, the game still has the weird mouse acceleration, so even with all of this fixed, and having a more precise sensitivity option through config file, it will still be impossible to set a proper sensitivity, but at least it would be closer than the in-game sensitivity slider.
gameVariable.xml