Galleries support alt text for images, e.g.,
<gallery> File:Mars 23 aug 2003 hubble.jpg|Mars|alt=the red planet File:Jupiter New Horizons.jpg|Jupiter|alt=a striped planet </gallery>
If you try to edit this in the visual editor, the current gallery tool gives you a "caption" of Mars|alt=the red planet.
Could it be made to work like the Media Settings dialog, with a separate field for the alt text, instead?