This is a web accessibility issue. We ought be providing alt text for images (especially those whose only content is a link, otherwise it outputs the file name as alt text). It has also recently become a requirement for FA. See http://en.wikipedia.org/wiki/Wikipedia:Alternate_text_for_images
Rather than reproducing the alternate text every time the image is called, it would be useful to provide it at the file description page, with a magic word or template and for it to be provided as the default alt text whenever it the image is displayed.
When I asked at the village pump, MZMcBride told me "It sounds as though you want a modification made to the image table to store alt text in a column."
Ideally, we should be able to override the alt-text contained at the image page with local code. So, say at [[File:Foo.png]], we had something like
{{DEFAULTALT:A picture of a typical sized foo on a blue background.}}Whenever Image:Foo.png was called, this would be the alt-text provided for screen readers and the like. However if you needed some different alt text (perhaps this is an article on Foo in general and you need to describe each foo at greater length), you could provide it in the usual way.
[[File:Foo.png|alt=A typical sized foo on a blue background. This particular foo is shaped like a bar.]]
The alternative is having bots editing every page that uses the image and inserting the alt-text, obviously this way would make things much, much easier.
This is about a generic MediaWiki feature. See T166094: Allow editors to provide default alt text on Wikimedia Commons file description pages about doing the same thing on Wikimedia Commons (or more generally on wikis which are Wikibase repos with the WikibaseMediaInfo extension installed).