I guess the articles I tend to edit must be unusually low traffic if you feel 24 hours is sufficient to conclusively determine consensus on some editorial question. Sorry for butting in.
It's enough time to determine if more time is needed. Admins are selected for their good judgement - try trusting them. The deleting admin just needs to click on the link to the article in the fair use rationale (if it doesn't state the article [and it's not just that the image page has been edited recently], then the image should be deleted straight away), and see if the removal was controversial. If some controversy starts after the 24 hours is up, then the image can be re-uploaded, or undeleted. Neither is much work. I would imagine any admin would undelete an image under such circumstances if asked.