Hell of a bump…
The reason it doesn’t by default is because it would have to find all references to those initial assets and update them as well, which requires resaving. Say a blueprint references a material you want to move, it has to be resaved with the new asset path. You can delete files too, but again you will have to check out all referencing assets to clear those references (usually Unreal will tell you to clear the reference first). You have to fix the references and then fix up redirectors in the case of deletion.
If you’re project uses source control (which most probably are), this means checking out and resaving all those files. This can result in bloating your source control depot. What I would like is a checkbox option to have that be the default behaviour if you don’t care about bloat.
When you move files, right-click the folder and hit ‘Fix Up Redirectors’. This will bring up a dialog box showing all the assets that also need to be saved with new asset paths. This didn’t work for me very well a few years ago when this thread was made, but it works perfectly fine now.
You may have to manually clean up folders in Windows Explorer as the folders are created by the OS, but the redirectors themselves should be gone. Generally speaking, it’s better practice to maintain a good folder structure from the very start of a project so you don’t have to do stuff like this often.