The short answer: No.
It is true, the WordPress Media Library is like one of those shoe boxes from the old days filled with pictures. Photos are added on top of the previous ones. There is no way to find a photo by tag or date taken. Well, it isn’t as bad as it seem, but first back to the answer.
The Media Library contains your images that you uploaded for use in posts. If you reorganized the contents of the library, moving photos into new folders by subject or some other indexing method, the URL of the images would change. Since the current URLs are used in your blog posts, those links would be broken. Your old posts would be all messed up. (That is not entirely correct, but I will leave that as a mystery statement for now.) Do not try to reorganize your Media Library even when it gets close to your storage limit with thousands of pictures. But don’t be disappointed that you can’t reorganize your library.
Here is the good news
Clearly you want to reorganize so you can find an image quickly. You actually can. Your photos are in reverse order of upload date. The most recent is at the top of the library. The very first image you uploaded is last. By default WordPress creates a folder for each month in which you upload images. You can easily reach any of those folders by clicking the All dates field. A drop-down menu lets you pick the folder for any month.
This brings up the photos you uploaded in the selected month.
But wait, there is more!
There is a Search field. Just type in that field and the images with matching text in their data fields, like Title or Caption, will be displayed.
The illustration here shows that the text “fl” was typed in the Search field. Two images come up.
Here is the first one:
The matching “fl” is in the word “Butterflies” – the text does not have to be at the start of a word, it can be inside! The other images was a match because the word “Reflections” was in the title. Pretty neat, wouldn’t you agree? See, you really don’t need to reorganize!
© 2017 Ludwig Keck