Is there no way to move old existing albums directly into new folders in iPhone's iOS v17.3.1's Photos app?

Only the hard way:

Select all items in an existing Album you wanted to move; copy them.

Create a new Album of the same name inside the new Folder.

Paste the items into the new Album.

Remove the original Album.

Repeat for each additional Album you wanted to move.

I don't disagree with you.

It is much easier on macOS than on iOS or iPadOS. I do that sort of reorganization on a Mac and let iCloud Photos sync it to my iPhone and iPad.

I would modify the procedure slightly, Mark. If you copy the photos from the previous albums, the copy will be a duplicate version when we add it, afaik. I prefer to select the photos in the existing album to add them to the new album.

I would create a new album with the same name in the new folder or subfolder, then use the command "Add Photos" from the (∙∙∙) menü in the upper right corner. This will open the list of all albums and we can easily access the album where the photos are currently added to and select them to add them to the new album.

On the mobile devices with iOS or iPadOS or watchOS it is unfortunately still necessary to plan our folder structure with all albums in advance, as we cannot move albums between folders. we should do that anyway, when we set up our Photos Library, but it is difficult to correct our initial design this way, when we notice later that we need more subfolders. On the mobile devices the albums are still a construction site and need some additional features. On my mobile devices the folders are nearly all empty, because most of my albums are smart albums and I cannot see them on my mobile devices. This is very wasteful.

Yes, "Add Photos" while in the new Album and selecting content from the old Album is more straightforward, léonie. I'm not sure I agree about the duplication issue, though. Have you observed a measurable storage usage difference in iOS?

When we duplicate a photo it will create a new version, but use the same original. It should not increase the storage considerably, but duplicate versions will no longer share the adjustments and previews, which might be confusing.

Sorry for the poor terminology, Mark, for me "Copy" always copied the file, not the reference, so I have used it as synonyms. But you are right, when I tested again, pasting to an album is only pasting the reference.

I wasn't suggesting using Duplicate. I suggested using Copy and Paste, but I like your suggestion of using Add Photos better.