This could either happen in Wikipedia articles on a per-thumbnail basis, or on Commons on a per-image basis (related: T166094: Allow editors to provide default alt text on Wikimedia Commons file description pages). Those are somewhat complimentary in that good alt text is sometimes contextual (the enwiki manual of style has some good examples).

My personal feeling is that this is a somewhat hard task that's not very motivating for a random newcomer wanting to expand Wikipedia (no visible change in the article) while there groups of people interested specifically in improving image accessibility so a standalone tool for adding alt text would make more sense than something aimed at generic newcomers.

This is also captured in the existing task https://phabricator.wikimedia.org/T296820 to add ALT text as part of the add image task.

As a note, the new ALT text property was recently added to wikidata and T166094: Allow editors to provide default alt text on Wikimedia Commons file description pages resolved, so it may make more sense to create this as a task that is specific to a Commons version of the Suggested edits feed.

Moving to Triaged, cc @KStoller-WMF in case you want to place this under an upcoming epic or otherwise consider for future work.