Example: a biography page with a picture of the person. The image contains no useful information, yet it adds enough emotional value to the page that simply removing it is not the solution.
If you set the alt text to the empty string "", that would prevent users browsing with screen readers from having to hear useless information like "a picture of John Doe, CEO" when that information is already present elsewhere on the page. However, it would prevent users with extremely slow connections (such as on tablets in rural areas) from knowing what the image would be before they finished downloading it.
If you give the image alt text, then the problems would be reversed. Users with extremely slow connections would know what they were downloading before it loaded, but blind users would have to listen to text that conveys no additional information.
Supposing that each of the two user types holds an equal stake in your site, should the images be given alt text when they contain no additional information yet appear in the main page content?