make path relative / absolute should also update output paths

Depends. In a studio setup images and linked scenes are stored in a repository and you would like it to use relative paths here. Render output can be stored on a network share so more departments can use it directly.

If consistency is your only goal it might not be as effective as you might think. Perhaps adding a new menu item to update both linked media and render outputs would work better. But not sure how much that menu item would be used at all.

So question is what are you trying to solve. Inconsistency or do you have an useful case. If the later, perhaps focus more what the benefits are.