So far the claimed failure reason is not visible in the build result, it was put into img's title only.

see code https://github.com/jenkinsci/claim-plugin/blob/master/src/main/resources/hudson/plugins/claim/AbstractClaimBuildAction/badge.jelly

As the user, if I can see the failure reason in build result directly without hovering over the image, I don't need to click inside to check detail

And it is even better, if the text can be set in own css (like yellow background/white foreground), it can be highlight.

Surely this could be optional to keep backward compatibility. It is user's responsibility to control the text size not too long to fit into build result space.