Work is being done to add taxonomies to the media library WP core
I will add a few screenshots from various media management plugins on how I envision categories and tags in the media library.
The question is why?
There is a great need to add some kind of ordering of media. One way is to add categories in the media library so the user can create some order by grouping images into categories and perhaps even tags. As I run this web site I today use Enhanced Media Library plugin for ordering the images that I use. Including categories in core will be very helpful.
The default Media library view as seen today:
Some examples on using Categories and tags in the media library.
This plugin adds Media Categories and Media Tags as can be seen in the left sidebar under Media. As well as filtering for All Categories and All Tags.
Bulk select is also something that needs improvement. Here it would be good to include a simple way to attach multiple media items to a category or tag.
Here are examples on clicking an image having it open in its own screen called Attachment Media.
Another example from https://wordpress.org/plugins/wp-media-category-management/
The above shows some examples on adding taxonomy such as category and tags to the media library.
I am thinking that this approach is something that would be suitable for WordPress Core.
I will likely add on to this article when more work is happening.