From an SEO point which is better for Media & attachment URLs.
a) Redirect attachment URLs to the attachment itself?
b) Show Media in search results?
Not showing Media in the search results would technically mean those will have a noindex robots meta and will be excluded from XML sitemaps.
Recently got an index coverage issue message in the search console stating a few media URL`s seems to be a Soft 404.
Selected answers from the Dumb SEO Questions G+ community.
Alan Bleiweiss: Soft 404 means they temporarily couldn`t reach the URL. If you test and find the URLs work, nothing to do.
Also, they recently said they were dealing with an internal Google error causing false soft 404 status.
Michael Martinez: I haven`t seen any truly useful indexing issue messages from Search Console in the past couple of months. I have received many notifications for non-existing problems, so there is a bug in Google`s system. That said, you can control how the media on a WordPress site is indexed by how you embed it on the page. If you don`t see any use for publishing an attachment page then just use embedded URLs (not linking them to anything). The images will ALWAYS be indexed as images unless you block the crawlers from your /uploads/ directory. I would not redirect an image URL to an attachment page as that would break the attachment page (it sets up an endless loop).
Razvan Alexa: The use of image indexing is to appear in the google search results for images. I always make sure the alt tag contains my keywords and brand and just let them be indexed normally, like Michael Martinez states above